That presumes the predator would only eat Pandas, which isn't realistic. Tigers and leopards both existed in the panda's historical range and did/do eat pandas. Smaller predators have been known to take panda cubs.
What else eats bamboo? Little competition could be an advantage, bamboo grows quickly, and the sedentary nature and stored energy permits the Panda to survive periodic reductions in bamboo availability. It is doubtless a vulnerability. A bamboo killing fungus would probably kill the panda too.
Yes, digesting bamboo has its positives, but eating almost nothing but bamboo has big negatives. There is little nutritional value in it. Its odd that Pandas are genetically and functionally omnivores and can digest meat and other plants, they just oddly choose not to. A very odd adaptation that I can't even suppose any advantage to.
By comparison, consider the hoofed rat (aka whitetail deer). It overbreeds, and then starves absent predation. Hunting rules change to adapt to wide variation in its numbers, in an attempt to reduce mass starvation incidents.
I'm not sure there is any proof of natural overpopulation. Deer, like many species, have been greatly augmented by mankind. We create large amounts of available food and we have killed of their primary predators. Meanwhile, we limit our predation on them to protect the newest generation.
Pressure from natural overpopulation is thought to be a reason for large animals on islands to get smaller. The pygmy elephant from Java being an example.
Another reason for pressure from over population is destruction of habitat. Either affects a species the same way as it is the ratio that describes the pressure.
On the other hand, being freed from competition or predation seems to give some species an opportunity to get larger. Rats on islands (sometimes the same islands as where the pygmy elephant evolved) often get bigger. The Moa of New Zealand may be an example of this also.
It is hard to predict what will happen in any particular event. It is easy to backtrack that big rats evolved from smaller rats, or small elephants evolved from normal elephants.