Best improv weapons will depend on your environment and what's available.
Do a search on my user name and rocks. Evidence from experts suggest that many more people were killed from thrown rocks than swords on historical Japanese battlefields.
If your prey is small enough, blowguns are easy to make. You can use beads, cotton, ball bearings, or any number of other items to make your darts/projectiles. I've seen them made from conical paper cups and screws, as well as matches, cotton balls, needles, and tape, to name just two improvised methods. Beads and needles, nails, or wire is another easy method. If you're near water, a small animal can net you a little food, plus bait for fish or other aquatic edibles...or guts for snares, if you're not near water. More guts= more bait.
A scarf and a big rock or chunk of brick or concrete can be used to kill anything smaller than a deer. Maybe even a deer at very close range, with enough practice. You can certainly stop a man who doesn't have any projectiles with such an improvised sling.
Enough spears and practice can stop anything smaller than a buffalo. Enough large enough spears can stop anything smaller than an elephant. Not my first choice, but good tactics and enough footage of sharp wood between you and a threat works pretty well.
John