How can I make terminal applications immune to terminal emulator close, but still able to use all virtual terminal features?

I see this must be something like screen, but without VT100 terminal emulation, something which will just apply whatever application does with "terminal proxy"'s terminal (like outputting something to stdout/stderr or using stty to set terminal options) to the terminal this proxy runs in.

// I know about screen and altscreen on, but it makes either this (screen with TERM=screen):

or this (screen with TERM=rxvt-unicode):

while I want this (rxvt-unicode without screen):

I have figured out that everything looks fine if I compile rxvt-unicode with USE=-xterm-color (in fact vim looks like on the second picture even without screen if I add this USE flag) and set TERM=screen-256color, but I do not like this workaround because it actually changes colors and I can't be sure that it will always change them only this way: