Packets do not get “cut-off” normally. That is kind of the point. Some protocols allow transparent fragmentation, but the fragments need to encode enough information for reconstruction, so you can still detect “less data received than encoded on send”.

You do not need bit error detection because you literally truncated the packet. The data is already lost. But in the process you learned it was due to MTU limits which is very useful. Protocols are already required to be robust to garbage that fails bit error detection anyways, so it is not “required” to always have valid integrity tags. You could transparently re-encode bit error detection on the truncated packet if you so desire to ensure data integrity of the “MTU resulted in truncation” packet that you are now forwarding, but again, not necessary.

Any end-to-end protocol that encodes the intended data size in-band can use this technique across truncating transport layers. And any protocol which does so already requires implementations to not blindly trust the in-band value otherwise you get trivial buffer overflows. So, all non-grossly insecure client implementations should already be able to safely handle MTU truncation if they received it (they would just not be able to use that for MTU discovery until they are updated). The only thing you need is routers to truncate instead of drop and then you can slowly update client implementations to take advantage of the new feature since this middlebox change should not break any existing implementations unless they are inexcusably insecure.

I don’t think you understand what normally looks like if you start forwarding damaged frames like this because you can’t tell the difference. That was the point.