Our daughter's school (20 years ago) did the Teddy Bear thing a little differently. It was started in the main Summer holiday and the Bear was sort of put out to tender from the beginning. The teacher chose one family that were off somewhere quite exciting and it was then their duty to pass it on to someone else. Every time it had a new 'carer' they were expected to fill in its 'passport' with details and photographs and also to post a card back to the school. The Bear had an amazing time and was only ever in the hands of people who really wanted the responsibility whilst the children had the fun of plotting his route back home from the postcards etc that came back. The goodwill of, sometimes, perfect strangers to pack the little fellow (he was deliberately a small one so as not to take up too much space) into their luggage and enter into the spirit of his adventures was amazing. The children got a huge amount out of his adventures and it was the talk of the year.
Being moved along by someone who "wants your place".