The real estate investment trusts that own the malls and shopping centers where many Sears stores are anchor tenants have waited years for the retailer's demise to renovate the sites and boost rent, although redevelopment costs may strain some plans.

Most large U.S. malls are controlled by REITs. In recent years, the REITs have cut their exposure to Sears Holdings Corp., which filed for Chapter 11 bankruptcy on Monday. Sears said it plans to close 142 stores.

Sears now accounts for less than 1.0 percent of many REITs' base rental income. Gaining control of vacated sites will be costly, while rebuilding the stores can run about $10 million to $12 million, or about $100 per square foot, for each site.