Limits by Bank on Seller Assisted Closing Costs?

[Ken Sanders]

I'm selling a house right now for $294k with a $10k seller assist.

The agreement states:

SELLER ASSIST - Seller will pay $10,000 toward Buyer's costs, as permitted by the mortgage lender, if any. Seller is only obligated to pay up to the amount which is approved by the mortage lender.

Do lenders usually put a cap on the amount of allowable seller assistance? If so, what happens if they don't allow the entire $10k?

Am I correct in thinking that the buyer is still obligated to proceed with the deal (otherwise losing their deposit since the contingency period is over) and that I only have to seller assist up to the lender's max?