Q. If an expensive hearing aid falls out and breaks on Shabbos,(one stept on it) can one pick it up? What should be done with it, whether inside or outside of the Eruv?
A. Horav Shlomo Miller's Shlit'a opinion is that it is muktza and should not be touched. Although, 'tiltul min hatza'ad' or indirect and unusual handling is some times permitted. See question 1770 regarding removal of a spider by having it climb a large piece of paper or cardboard, where it is not trapped and then promptly throwing it outside. However, in this particular case it is for the need of saving the muktza object and it is not permitted.
If the hearing aid landed outside where there is no Eruv, and it involves a significant loss, one may push it with the shoe, less than four amos (about two meters) at the time, until one finds a place in the street where it may stay hidden and protected until the end of Shabbos.
Rabbi A. Bartfeld as advised by Horav Shlomo Miller and Horav Aharon Miller Shlit'a