Rotech Healthcare Inc., a provider of home respiratory products, has filed for bankruptcy, saying that its plan to cut its debt by about half and to reorganize is supported by a majority of its noteholders, Bloomberg News reported yesterday. Under the proposed reorganization plan, the company’s lenders, owed $23.5 million, and first-lien noteholders, owed $230 million, will receive an amended term loan. Second-lien noteholders will get all of the shares in the new Rotech, eliminating more than $300 million in debt, according to a company statement. The company, based in Orlando, Fla., said that it has more than $100 million in assets and owes lenders and noteholders about $543.5 million.