In a case like this, does that mean that Smyte (the company, even if they no longer own the trademark) still exists and is liable for all the penalties? Would they usually ask for the cash to pay for them as part of the asset purchase?
Don't know, not a lawyer.
At the end of the day, judges (and appellate panels) have to interpret the law and they don't function like automatons. They take into account the spirit of laws/contracts as well as the letter and most have enough common sense to get missed off at these naive tactics.
(All of this is a good reason i hate LLC's. They aren't necessary anymore to actually do risky innovation in 90%+ of cases. In a non-LLC, they shareholders would be liable, and then you'd still have someone to go after)
Usually, they would use the cash to wind down.