Most states impose limitations on the authority of the legislature to borrow money, to protect taxpayers and the credit of the state government.
I would not separate the “to protect …” phrase, which is actually used as an adverb modifying the verb “impose,” from that verb more than is necessary. The prepositional phrase “on the authority …” is used as an adjective modifying “limitations,” which it properly abuts. My solution is to move the adverbial phrase to the beginning of the sentence, The reworked sentence follows.
To protect taxpayers and the credit of the state governments, most states impose limitations on the authority of their legislatures to borrow money.
