LOS ANGELES, United States — American Apparel LLC started to lay off staff on Monday, after Canada's Gildan Activewear Inc withdrew its initial plan to buy some of the bankrupt US fashion retailer's manufacturing operations, people familiar with the matter said.Gildan won the rights to American Apparel's brand with a $88-million bid in a bankruptcy auction last week. It had previously indicated it would assume some of its manufacturing operations, which had made the brand synonymous to "Made in the USA."Many of the 2,166 employees at the company's headquarters in Los Angeles and 959 employees at the nearby South Gate manufacturing facility now stand to lose their jobs, the sources said, asking not to be identified disclosing these details to the media."The company issued a WARN Act notice several months ago, letting employees know that depending on the buyer of the business, a sale could result in eventual shrinkage of some business areas," American Apparel said in a statement."The company is pleased that it was able to secure a second agreement with (textile manufacture) Broncs, which plans to save over 300 jobs when they take over the Garden Grove facility," the statement added.Gildan had already indicated it would not take any of American Apparel's 110 stores.By Jessica DiNapoli; editor: Nick Zieminski.