(My field is pure mathematics)
EDIT: I asked this question as a form of thinking out loud. I've realised with the help of the commenters below that my inclinations were a bit stupid, but others in similar positions might find the discussion useful.
I have an honorary, 'visiting' affiliation with the university (in my city where I live) where I once had an academic position. I do not have a paid research position there, and the adjunct teaching positions I have had of late in the mathematics department there appear to have run out. I have library and building access, and am for most intents and purposes counted as staff, minus the actual job. I have continued steadily publishing papers in this position.
I am wondering what people would advise about listing my affiliation on papers. I have no complaints with the department, and they have been happy to renew my status, which is very nice. However, I would like to signal in some way that I am not in fact employed to do this research. The only way I can think of this is to stop listing myself as being 'at' the university in question, but this seems to me as ungrateful, or risking losing this affiliation.
I am also aware that the department gains from my producing research and listing it as having taken place there, without the actual full cost of employing me. This may lead to certain negative incentives, but this is pure supposition.