Whether you have a seam pulling apart or a full-blown rip, you can fix most fabric tears with the right tools. If you’re the sort of person who travels with a bit of duct tape for emergencies, you can patch the area—but this fix isn’t going to last for long. A stronger solution is Gear Aid Tenacious Tape, ultra-strong repair tape that comes in five colors. For larger holes and tears, you can also try fabric glue and patches, or even try sewing it together—in a pinch, dental floss can be a sturdy, strong thread alternative.
There’s some advice out there saying that if your plastic hard-sided suitcase gets a dent, you can put a hot hairdryer on the offending spot for a few minutes and then, when it’s hot and pliable, push it back into place. That sounds like a recipe for noxious fumes, so proceed at your own risk.