Two items that I have used for emergency repairs are dental floss and clothing tags. Both items are surprisingly strong and long-lasting. You always have clothing tags available and the dental floss doesn't take much room, and is light. The extra dental floss and an awl are possible choices for a bug out bag also.
Most of the time I carry extra dental floss with me for the purpose of emergency repairs, especially when travelling. I have had occasion to use them for repairing backpacks, luggage and footgear. Repair shops for these items have never been available when I needed them. I either didn't have the extra funds for replacement, or they were not available at the right time.
I always use waxed dental floss because it is stronger and lasts better. Dental floss looks terrible on most luggage, backpacks and shoes because it is only white or pale green and does not match much luggage, etc. I got around this problem by using leather shoe dye, permanent marker, or paint.
I ordinarily carry a punch or awl as part of my emergency supplies, as well as needles and thread. That takes care of the being able to sew part of the repair. I usually make a duct tape and cardboard cover for the tip of the punch, for when it is packed away.
Necessity was the mother of invention for the use of the clothing tags part of my impromptu repairs. I did this the first time when my backpack strap gave out on a trip. I had nothing I could spare for materials to patch the part of the backpack strap where it had frayed.
The only thing that I could think of was a clothing tag that matched the color of the backpack. I cut the tag off and sewed it over the frayed gap in the backpack strap. The clothing tag worked just fine and outlasted the rest of the backpack.
I don't know whether you have noticed how strong clothing tags are. If we could buy clothing made out of the same stuff the tags are made of, we could wear those clothes for the rest of our lives.