Do you have a clause in your MSA or Agreement with the vendor that requires them to provide financials? If you do, withhold payment or use any means allowed by your agreement. If not and it's an existing vendor, there isn't much you can do legally.
Prior to revamping our vendor onboarding we reached out to a few legacy vendors and let them know that we would be requiring financials with a revised MSA when their current agreement expires. Any vendor that didn't agree well in advance of their agreement expiration, we made plans to replace and submitted official notice that we were opting out of any future renewals. All but one provided financials within thirty days.
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"100 victories in 100 battles isnt the most skillful. Subduing the other's military w/o battle is the most skillful." Sun-Tzu