Will publisher waive fee if currently unaffiliated?

This surely depends on the journal, and probably on your specific case (I don't imagine it's common to have a blanket waiver for authors without affiliation). Many journals do provide support to authors without funding. For instance, look at the PLOS FAQ #4:

https://www.plos.org/publications/publication-fees/

Publication Fee Assistance is intended for authors who demonstrate financial need. [...] PLOS considers applications on a case-by-case basis.

Try looking at the webpages for journals you're considering for such information. If you can't find anything, you can try contacting the journal.

Being unaffiliated is not always sufficient grounds for a fee waiver. However, most journals do consider waiving off the publication fees if the author is genuinely not in a position to pay the fees. You should write to the journal explaining that you are currently unaffiliated and do not have sufficient funds to pay the fee. If the journal is convinced, you might get a partial or complete fee waiver.