In my time as a trombonist, I don't think I've ever seen this marking, but perusing my dictionary this week I found it there waiting for me. It means to play the marked passage "in the manner of sobbing", usually characterized by a gliding between notes.
The trombone being what it is, you'd think we'd get to play singhiozzando at least sometime -- we're pros at gliding! Maybe composers just don't think we can pull off the "sobbing" effect. Sigh!