In the Netherlands it seems the affected coalition party does not have to be consulted in some cases. Specifically, I will argue this may be the case in the following two situations
When the official in question accepts the dismissal and their party did not supply the prime minister or any of the deputy prime ministers. In this case the dismissed official would have to agree with the dismissal (and this may be seen as a deviation from the official procedure).
When the dismissed official is a state secretary and their party did not supply the prime minister or any of the ministers. In this situation the affected party would not be consulted even when strictly following official procedure.
Dismissal without consulting the Council of Ministers but with agreement of the dismissed official
To elaborate this, I will use one specific example. In that case a high ranking member of the affected party was consulted, but based on the arguments given by the prime minister (who dismissed a junior minister, or staatssecretaris in Dutch) the affected party does not have to be consulted depending on the coalition. It's a bit complicated, but I'll explain the reasoning.
Let's lay out a few definitions first:
The prime minister who is the head of government in the Netherlands.
The Council of Ministers is made up of all the ministers (including the prime ministers) and the deputy prime ministers.
The deputy prime ministers are normally made up of one representative from each coalition partner. This doesn't have to happen, for example in Rutte I (2010-2012) only the Christen Democrat Party (21 seats) had a deputy prime minister while the other coalition party, the Freedom Party (24 seats), did not get a deputy prime minister (and they did not hold any minister or state secretary positions either).
Now, let's look at the dismissal process. For this I'll cite the dismissal of Mona Keijzer who was the State Secretary for Economic Affairs and Climate Policy. She was dismissed in September of 2021 over her comments on the cabinet's Covid policy.
Officially (per the Rules of Order for the Council of Ministers Article 4.2.K.), the prime minister can nominate ministers and state secretary for dismissal. These nominations are then decided on by the Council of Ministers.
In the case of Mona Keijzer's dismissal, the full Council of Ministers was not consulted (source in Dutch). Instead, the deputy prime ministers and State Secretary Keijzer agreed with the dismissal without the full Council of Ministers having been consulted. The PM was asked about this in parliament, and the state broadcaster NOS reported the exchange as follows (Mr. Omtzigt is an MP from Keijzer's party)
Ook Kamerlid Omtzigt zette vraagtekens bij de manier waarop Rutte het ontslag heeft aangepakt. Hij stelde dat de ministerraad er met meerderheid van stemmen over had moeten beslissen. Rutte bestreed dit en zei dat het voldoende is om de knoop door te hakken met de verantwoordelijke minister van Economische Zaken en de drie vicepremiers.
Translated by me:
MP Omtzigt also questions the way [PM] Rutte handled the dismissal. He [Omtzigt] stated that the Council of Ministers should have voted on the dismissal by majority. [PM] Rutte rejected this and said that making the decision with the minister in question and the deputy prime ministers sufficed.
In my view, this situation is different from a minister resigning on their own accord, as the move to dismiss was instigated by the prime minister in response to a news paper interview by Mona Keijzer.
In this case, a senior member of the party in question was consulted. Indeed, Minister for Health de Jonge holds the position of deputy prime minister and he and Keijzer are both members of the Christian Democrat party.
It is possible though for someone to hold the minister position without having a deputy prime minister of the same party. For example, in 2020 Martin van Rijn of the Labor party was Minister for Health for over 4 months. In that case, he had been appointed following the burnout of the previous minister and his experience as a civil servant and later state state secretary at the Ministry of Health (both preceding the cabinet terms in which he was appointed minister). The Labor party was not a member of the coalition government though.
Going further back, the Second Biesheuvel Cabinet in 1972 had support from the Christian Historical Union which supplied 3 minister positions and 2 state secretaries without having a deputy prime minister. The other two junior coalition partners did have deputy prime ministers.
With that background information, we can finally answer the question. The dismissal without consulting higher-ups in the party of the dismissed official may be the case when a small coalition party does have ministers or state secretaries but does not hold a deputy prime minister position. From the Freedom Party (coalition partner without ministers or state secretaries), Labor Party (minister from a party which is not part of the coalition) and Biesheuvel Cabinet (junior coalition party with ministers and state secretaries but no deputy prime minister) examples we can reason that this is possible, though it has not happened recently. In such a situation, the dismissal could take place following the aforementioned Mona Keijzer example in which only the deputy prime ministers and the dismissed official are consulted and agree to the PM's dismissal proposal.
Dismissal of a state secretary by consulting the Council of Ministers which does not have anyone from the dismissed official's party
For this situation to apply, the situation would have to be as follows:
A junior coalition party supplies one or more state secretaries but no minister, deputy prime minister or prime minister positions.
The state secretary from that junior coalition party is dismissed by a vote in the Council of Ministers.
Since the Council of Ministers does not have anyone from the junior coalition party (state secretary are not included), nobody from the dismissed state secretary's party would have to be involved in the formal dismissal process (described in a bit more detail in the previous scenario).
Of course, this situation would be unlikely in practice. If there is such a junior coalition party then the coalition probably relies on this party's support to pass legislation. By dismissing one of their state secretaries and given that they have no ministers or deputy prime ministers it is unlikely that they would continue to support the coalition despite the dismissal.
On the other hand, this might be possible if the coalition is breaking with the party of the dismissed state secretary anyway (and they're breaking up on bad terms). Another scenario would be when the dismissal is urgent and the Council of Ministers prioritizes the dismissal over interparty formalities (e.g. when the state secretary's behavior is so contemptful and ongoing that they assume their party will stand behind the dismissal anyway).