Possibly the sync begins a one-shot cycle. The sync is an upward going edge, which produces a brief spike through the capacitor. It turns on the NPN, sending a 100nS pulse, then ending the timing cycle. Quickly the diode discharges the capacitor, and also pulls the NPN bias low (or lower) to prevent oscillations. If the sync circuit is omitted then oscillations happen.
Your schematic resembles a complementary multivibrator found at the webpage below (a collection of different multivibrator circuits). The caption states that the classic astable (usually drawn with NPN's) can be rearranged to use PNP's, or a combination of both types.
https://www.4qdtec.com/mvibs.html