Look for spots to open up the pot when it's folded to you.
Look for spots to steal blinds and to re-steal if you're in the blind yourself.
Look for spots to make squeeze plays in late position.
Look for spots you can make a big raise/shove in late position vs a bunch of limpers.
3bet raise/shove over a preflop raiser with anything decent and try to pick up the pot preflop or hope your hand goes up.
Don't be afraid to take flips.
Try to use your tight image to your advantage.
I think when you're card dead, taking advantage of opportunities to pick up pots are more important than waiting for a big hand to come along. So, use that tight image. Steal from the blinds. Don't be afraid to shove against preflop raisers and take flips; especially when you're dropping below 10 BBs. Sometimes, you can't rely on the cards to help you out and the blinds wont stop raising, making your stack shorter each time. Sometimes you gotta take it upon yourself to make plays if you want to survive.
Finally, don't think too much into it. Everyone gets card dead at some point and it's not that big of a deal. Sometimes, you just don't catch cards. So, just play tight, pick your spots, and hope for the best. If it doesn't work out, there are plenty of other tournaments to play.