I don't think I'd actually sit out....but I'd probably decide to play super tight and start doing something else on my computer. watch a movie or something. if I pick up premium hands I'll play, if I get to see a flop in my BB, great. Probably try to steal blinds a couple times in late position just to keep up..
I have, in a super satellite "effectively" sat out. I had a comfortable stack on the bubble and there were a couple short stacks and as soon as the bubble burst we were all going to make $3,500 off a $400 buy in. So, I looked at my cards with 100% intention to fold every single hand except AA...and if a biggish stack raised before me, I fully intended to fold the AA too... A couple times I got to see a flop in my BB, the weak-tight SB would limp in, then check the flop so sometimes if I completely missed, I'd bet half the pot and he'd fold. sometimes I'd just check it down with him to the river if I had bottom pair or something. Surprisingly, it took about 45 minutes of this strategy to bust one short stack! Guess what he went all in with? AA....and he lost....that's a bummer, man!