As others have said they already have open borders, free movement, shared currency, and free trade with their ‘parent’ nation, and by extension the EU.
Effectively the mico-nations gain all the benefits of EU membership without having to actually be a member. Not being official EU members allows them advantages, such as the ability to set taxes below the legal limit, that they have exploited to become very rich.
Much of the more thought out thinking about Brexit also revolves around the UK taking a similar approach. Managing to exploit the advantages of EU membership whilst at the same time getting ahead of the other members via being able to offer lower taxes and regulations. The problem is of course, that with the micro-nations they have largely been able to fly under the radar. They are so small that the impact of their ‘cheating’ has been kept rather small, if they were larger than things would be quite different and they wouldn’t be allowed their favoured status.
Even as far as the micro nations the tide is turning and there is a big movement underway to reign in tax havens. It could be argued that this movement was born exactly out of larger nations also introducing laws that allowed for loop holes (the infamous double Dutch exemption using the Netherlands and Ireland) and had this not happened the micro-nations would continue to fly under the radar.
As things are however, there’s a lot of attention on the micro nations at the moment. We shouldn’t forget too that though the micro nations particularly stand out to laypeople due to their legal status as separate nations, you also have a lot of other polities in a similar situation vis-a-vis the EU such as the Channel Islands, Caymans, etc…
Anyway, I’ve gone off on a ramble here. The TLDR answer- the micro nations already get all the advantages of membership and many of the advantages of non-membership with their current situation. There’s never been much interest from either side in actual membership due to their situation where they are effectively tiny but highly special parts of France, Italy, Switzerland, and France/Spain.
Of the five micro nations Liechtenstein presents the most interesting case as though it is in practice effectively a semi-autonomous part of Switzerland, it nonetheless has a far greater legal presence internationally than other micronations, such as for example being a full member of the EFTA.
If Swiss membership of the EU were to ever become a serious prospect again (its fairly dead for the moment given Switzerland is also able to enjoy the best of both worlds in many ways) then there will be a genuine question of what to do with Liechtenstein.