Foudy was loaned to AHL Bridgeport on Saturday.
Foudy was called up by the Islanders on Tuesday.
Foudy was placed on waivers by New York on Sunday, Elliotte Friedman of Sportsnet reports.
Foudy signed a one-year, two-way contract with the Islanders on Wednesday, per PuckPedia.
Foudy didn't receive a qualifying offer ahead of Sunday's deadline and will now be an unrestricted free agent, Alex Daugherty of The Tennessean reports.
The Predators placed Foudy on waivers Thursday, according to Nick Kieser of Nashville Hockey Now.
Foudy registered his third point of the season with an assist in Saturday's 4-3 loss to the Rangers.
The Predators claimed Foudy off waivers from Columbus on Saturday, according to Elliotte Friedman of Sportsnet.
The Blue Jackets have designated Foudy a non-roster player and placed him on waivers Friday and will assign him to AHL Cleveland should no team claim him, Jeff Svoboda of the Blue Jackets' official site reports.
Foudy scored a goal on four shots in Tuesday's 4-3 loss to the Flyers in overtime.