The decision letter is Decyzja where it is stated the new resident card validity dates. The new card is not ready yet. The current one is expired.
I had that exact problem myself. I solved it by writing a letter (in the foreigners office so I could submit it immediately) asking for the card to be issued faster, on the basis that I needed to go back to the UK to visit my mother and had plane tickets booked.
The passport is Russian, which doesn't allow to travel anywhere in the EU without visa/residence permit.
Technically, you have a valid residency permit; you just don't have it yourself. However, I'm not sure how confident I'd feel about explaining that to, for example, French police.
Can someone confirm that a person can enter Poland with a valid decision letter and already expired karta pobytu?
You can do that; however, you might find it a problem to convince staff at an airport who do not speak Polish or understand the Polish visa system that they should let you get on a plane to Poland. That is the bit which would worry me, not the getting into Poland bit.