Can a loose tooth ever be stabilized in it's place?

Loose tooth from?: What's crucial to the answer to your question is. "why is the tooth loose?" is it from periodontal (gum) disease? Trauma? Occlusal trauma? Short root? Recent orthodontic treatment? Etc. The cause will determine treatment, if necessary. Merely stabilizing loose teeth may give false sense of security ; not address problem. Discuss with your own dentist who can e-valuate cause and suggest a solution.

Yes: A mobile tooth if it is not infected, can be attached to adjacent stronger teeth to stabilize the mobility.