The following is no legal advice, just what I remember from reading things here and there.
I believe that unemployment insurance doesn't have
a negative effect on re-entry. The only reason you could be denied coming back into the country for economic reasons is if the immigration inspector believes you are going to be a public charge. This only becomes an issue if several conditions are met:
1. You have to be asking for admission into the U.S. If you are a permanent resident and go out for a trip of less than six months you are not considered to be looking for admission into the U.S. so the public charge test doesn't apply.
2. You probably have to be unemployed at the time of returning, plus meeting point 1 to be an issue, or have already collected some federal money. It has been discussed in other places that unemployment insurance does not have anything to do with being a public charge, and I think it is fully funded by employers. The point is moot, as you mention correctly that none of this is an issue at the time of getting citizenship.
3. The inspector has to believe that you'll be a public charge. This is entirely subjective as far as I know, and taking to the extreme could be applied even to employed people, if the inspector has credible information that you'll become a public charge. Of course I have never heard of such a case. In fact, I have never heard of any case of denial of admission on public charge grounds.
I don't know how unemployment insurance works here, but in other places you are not supposed to collect it if you are not actively looking for work inside the country, i.e. if you travel outside you are supposed to get nothing, if you get money that could amount to insurance fraud.
Anyway, I fail to see that just collecting unemployment insurance would have any detrimental effect on your permanent resident status. Please enlighten us if you know something we don't know about this, because it would be extremely sad that a family may go hungry for fear to collect unemployment insurance because of fear, uncertainty and doubt created by your message.
My 2 cents.
