Some lawmakers, judges and regulators are trying to rein in the U.S. debt-collection industry's use of arrest warrants to recoup money owed by borrowers who are behind on credit-card payments, auto loans and other bills.

More than a third of all U.S. states allow borrowers who can't or won't pay to be jailed. Judges have signed off on more than 5,000 such warrants since the start of 2010 in nine counties with a total population of 13.6 million people, according to a tally by The Wall Street Journal of filings in those counties....