most teams may not find it very easy to trade their veteran players during the NFL draft since most teams don't have room to accommodate such players though exceptions are there to prove you wrong

I think it is always a hard decision what to do with aging players, especially once they've passed their peak. The problem is that they are only going to get older, so it's a bad investment to keep them. However, it can be hard to let go of a good player even if they player is aging. Also, there can be personal relationships involved.