Hi
I have a 2 room basement that was expanded int he past. One room has a foundation built of cinder blocks (at least the walls are). The other is poured concrete.
The joists rest on the cinder blocks walls and there is a RIM joist between them (perpendicular).
HVAC has two supplies running through holes in the RIM joist to Room 1.
The problem is that Room 1 has no returns and therefore isn't cooled /heated adequately.
I want to cut the RIM joist and run another hvac pipe as a return and wanted to confirm that it wouldn't cause any structural issues. The actual joists rest on the cinder block wall from what I can tell with a wood plate (sill?) between the cinder and the joists

Forgot to include a picture of the existing HVAC pipe (I cut a hole in the drywall ceiling to see into the wall /ceiling cavity)

If the rim joist is fully supported by a structural wall underneath (be it block, poured concrete or even wooden framing) then yes, you can cut through it to install the new duct.

Technically, if there is finished space on the other side of that 'rim joist' then it is no longer a rim joist, just a joist with a support wall underneath it.