This is very common when using a vibrato arm and lowering the note making the string very loose and flexible. If the string gets snagged under the lip of the pickup it is most likely that the winding in the coil got damaged and would need to be repaired by a qualified repairman. This is more common with humbuckers when the covers are removed and can happen without using a vibrato to lower the tension on the note. Normally single coil pickups have covers as it is an important protection to the coil wound around the rod magnets on typical Fender style single coil pickups. My first experience was caused by a country singer using my 1956 Telecaster and they got the high E string snagged under the lip of the bridge pickup. It was my start of rewinding and repairing pickups.