Not being privy to the negotiations, I can't give an absolute answer but my guess would be that in any negotiation, the two sides know pretty much what the other side wants.
I'd say the EU understands that May needs things that will get the ERG and DUP to play ball, so these would be concessions on the Irish border (never going to happen) and disappearing up its own arse (I think the ERG only want things that are impossible from the EU because they dogmatically hate it, the EU can offer literally nothing other than ceasing to exist that will please them). Given those insights, when the EU says it won't be offering fresh proposals, I think it's talking about on these areas.
If Labour were the government, they've already made it clear their ideas on a leaving package would be different from the tory ones. The NI border, for one, wouldn't come into play if Keir Starmer's famous customs union were agreed, so I think, if government changed, there probably would be a willingness in the EU to renegotiate.