Can a person who lives abroad be a trustee or a beneficiary of a trust?

The answer is yes and no. It really does depend upon the jurisdiction. Certainly, if your children or the person you want to be a trustee, lives in France or Spain, or the USA, definitely not. You shouldn't appoint them as a trustee because there are issues during lifetime before there's even any assets in that trust. They definitely cannot be a trustee. Generally speaking, your trustee should be based in the UK, because we have no idea how rules may change in the future for other tax jurisdictions.

In terms of beneficiaries, it doesn't matter where somebody lives for them to be a beneficiary of a trust. Very rarely are there any issues around benefiting from a trust because it's exactly the same as if you pass the assets directly to them - they would get the benefits whether they come from a trust or directly.

Trustees have the more UK base but beneficiaries worldwide are absolutely no problem at all.