Like a lot of situations in real estate, I believe what I would do would depend on a lot of factors:
How good of a deal is this?Are you buying at 100% of ARV or 50% or ???
How strongly motivated is the seller and does the seller have other buyers waiting in the wings?
Is the seller getting cash at closing or not? If so, are they in a hurry to get it?
Is there anything being left behind that is considered dangerous and/or restricted to specialized and/or expensive disposal?
Is there anything that needs to be disposed of that code enforcement could take serious issue with were it to remain in view?
I’ve been in these situations in the past and, fortunately, had most of the “cards” in my favor. A generous escrow (i.e., one that I believe exceeded my costs to cure by at least 50% and, preferably, 100%) and a relatively short fuse for the seller to cure has worked every time (so far). The escrow provisions gave me the money and the obligation to cure if the seller didn’t perform. The extra money the seller has on the line is usually a great motivator.
Being a conservative investor, the one thing that would stop me from closing (even with a good escrow agreement and plenty of cash to cover the cleanup) would be a situation I considered to have a reasonable risk of someone getting injured or killed due to the nature of the material left behind and easy access to it.