'become indebted' is a correct and usable phrase in written English.
You can use it to describe a situation in which somebody owes money or some other form of debt, either literally or figuratively. Example: After his financial troubles, Paul had no choice but to become indebted to the bank.
We have now become indebted for conclusive light on this subject to Mr. John Dewey, the philosopher.
"They have become indebted relative to their wealth rather than their incomes, and that is a built-in vulnerability".
But it had not been shown to them how serious the country had become indebted, and how recklessly capital had been transferred and used in the economy.
Communists have accused him of whipping up threats of another coup attempt against Mrs. Aquino so that the civilian leadership would become indebted to him.
Paying them off in just two weeks is unaffordable for most borrowers, who become indebted long-term," Nick Bourke, Pew's expert on small-dollar loans, said in a prepared statement.
That the garnishee shall withhold and retain any property in which the debtor has a substantial nonexempt interest and for which the garnishee is or may become indebted to the judgment debtor pending further order of the court.
He partied hard and became indebted; in 1840 he owed £20,000 (around £2m today, or $3m).
In an earlier era, they became indebted to the pawnbroker; now they are indebted to banks or credit-card companies.
Indeed, the regime became indebted to some of them, and some developed close ties to the regime's topmost leaders.
Bourne, you'll recall, became indebted to the Guardian after getting one of its reporters killed on Waterloo station.
Work was withheld, the prosecution said, until tenants became indebted to the pair; that debt was used as a means of controlling them.
