The VC lends (the money from the bank) which the vc borrowed, to the clinic.
They are a sort of middle man. It the clinic is on the hook to the bank and the Vc takes fist cut before playing the bank.
Eg. The vc only risked the company they were buying, and gets paid first.
(Edit: To be clear, I agree with the other commenters that none of this is what VCs do. I'm just pointing out that the way this is being described doesn't even work on its own terms. Needless to say, LBOs are not "risk free".)
It does not happen overnight. But what happens is after they take control of the clinic or company they change the sales model to boost reoccurring revenue, this then allows the clinic or target company to take loans out. Because they look good on paper. The company then pays VC back when then pays bank back.
This can be done in about 6mo to 1 year process with some companies. The initial out of pocket expense is small and paid back very quickly.
I also forgot. Sometimes they will take the newly owned company and merge it. During that process they extract more money and load more debt onto the remaining entities, again making the VC money.
In some cases they can even get huge tax benefits by loading the company with debt which offsets the tax bill of the final entity.
When these transactions are done, within the span of a day multiple companies are created and merged and absolved.
There is little to no risk for the VC