Tzitzis can often get torn if one does not use sufficient care when laundering them. There are various patents in how to launder them without damage. However, sending them to a non-Jewish laundry can indeed create problems. One person reports that the laundry charged him a large sum and when queried they answered that “it was hard work undoing all those knots”. At least the tzitzis were not ruined – they could be reknotted. However in another story I heard, (I cannot vouch for its accuracy), the tzitzis beged was returned minus the tzitzis together with a note that the laundry had cut off the threads hanging from the corners – in this case the tzitzis threads were more than just torn!!