Does it matter for liability whether a carve-out happens before or after the sale actually closes?

Yes, considerably. A carve-out completed before closing means the unwanted asset or liability is already out of the target corporation by the time you buy its shares — you simply never own that piece, and there's nothing further to untangle after the fact. That's the safer, more standard sequencing, and it's why pre-closing carve-outs are typically made a condition you confirm is satisfied before you're obligated to close at all.

A carve-out attempted only after closing puts you in a very different position. Having already bought the whole corporation, including the unwanted piece, you now need a separate post-closing transaction to move it out, which requires its own agreement, its own consents, and takes real time to complete properly — and during that entire period, you own the unwanted piece and whatever liability comes with it, exposed exactly as if no carve-out had ever been planned.

If a carve-out matters to you, insisting it be completed and verified before closing, rather than promised for afterward, is the practical safeguard. A business lawyer can confirm the carve-out is actually done, not just agreed to, before you close.