Is the lender still insured even after the borrower stops making monthly MIP payments on a FHA loan?

Yes The insurance is pooled for this reason to protect the investor

The MIP payments on an FHA loan are combined with the monthly principle and interest payments. If the borrower stops making heir MIP payments they've basically stopped paying their mortgage and the mortgage company will start foreclosure proceeding depending on foreclosure laws for the state the property is in at thats when the mortgage insurance that the borrower has previously paid kicks in.