Expatriates are people who left their country of citizenship voluntarily for personal reasons (or children of such people).

Voluntarily is not necessarily the case - many people leave their country out of necessity, e.g., for economical or political reasons, and would not mind going back. Moreover, refugees are also expatriates.

This means that, while they may return, they are currently abroad. Whatever new laws are voted in in their home country mostly do not affect them in any way, with the exception of maybe some short visits.

Expatriates, especially when they do not have a second citizenship, are still subject to the laws of their country and affected by its policies. One example is the Americans living abroad but still required to pay the federal tax. Another example is the Russian students, who had to return home due to the closure of the university exchange programs in the last couple of months.

Another side of it is that the representative of the home country (usually the embassy) takes care of the expatriates, in case they are feel mistreated by their country of residence, or when they need to be helped/accounted for after natural disasters, terrorist attacks, etc.

It is true that the expatriates are not affected by the policies of their country in the same ways as those residing in the country itself, but they are affected anyway. At the minimum they are dependent on their country providing (and renewing) them with a valid travel document (such as a passport or a laissez-passez).

Yet when they are able to vote, their voice counts as much as the voice of someone actually living in the country.

What is the justification for an expatriate having democratic rights in their home country even after leaving it?

The most crucial point here is whether voting is seen as a right or as a privilege. If voting is regarded as a citizen's right, and the citizen has committed no crimes, this right cannot be revoked from them. However, some countries do adopt the attitude that voting is a privilege, granted to those living within the country (typically, more than the half of the calendar year). One example is Israel: the Israeli citizenship is accessible to anyone subject to antisemitism, including many people who have little knowledge of the local realities and/or have never lived in the country. For this reasons Israel allows voting only for the resident citizens - which is a matter of an ongoing political debate (e.g., see here).

Expatriates are people who left their country of citizenship voluntarily for personal reasons (or children of such people).

Voluntarily is not necessarily the case - many people leave their country out of necessity, e.g., for economical or political reasons, and would not mind going back. Moreover, refugees are also expatriates.

This means that, while they may return, they are currently abroad. Whatever new laws are voted in in their home country mostly do not affect them in any way, with the exception of maybe some short visits.

Expatriates, especially when they do not have a second citizenship, are still subject to the laws of their country and affected by its policies. One example is the Americans living abroad but still required to pay the federal tax. Another example is the Russian students, who had to return home due to the closure of the university exchange programs in the last couple of months.

Another side of it is that the representative of the home country (usually the embassy) takes care of the expatriates, in case they are mistreated by their country of residence, or when they need to be helped/accounted for after natural disasters, terrorist attacks, or otherwise find themselves in distress, etc.

It is true that the expatriates are not affected by the policies of their country in the same ways as those residing in the country itself, but they are affected anyway. At the minimum they are dependent on their country providing (and renewing) them with a valid travel document (such as a passport or a laissez-passez).

Yet when they are able to vote, their voice counts as much as the voice of someone actually living in the country.

What is the justification for an expatriate having democratic rights in their home country even after leaving it?

The most crucial point here is whether voting is seen as a right or as a privilege. If voting is regarded as a citizen's right, and the citizen has committed no crimes, this right cannot be revoked from them. However, some countries do adopt the attitude that voting is a privilege, granted to those living within the country (typically, more than the half of the calendar year). One example is Israel: the Israeli citizenship is accessible to anyone subject to antisemitism, including many people who have little knowledge of the local realities and/or have never lived in the country. For this reasons Israel allows voting only for the resident citizens - which is a matter of an ongoing political debate (e.g., see here).