There are many variables.
Foam surrounds from the 70’s and 80’s were notably fragile.
Capacitors in the crossover potentially can fail.
Foam surrounds on woofers and mids will fail, but it depends on your environmental conditions and the type of foam used. These typically last 15-20 years.
Rubber surrounds can last many decades. Woofers and mids with paper or treated cloth surrounds can last a lifetime.
There are some tweeters that have foam dampening hidden within their construction, these too will eventually deteriorate and gum up the works. Luckily this is not as wide spread as foam surrounds. For many compression drivers with aluminum diaphragms, the surround is made of the diaphragm's material pleated in one pattern or another. The aluminum will work harden over time and will eventually fail.
For crossovers, the most common failure is electrolytic caps deteriorating with age and requiring replacement. Many vintage "oil" caps last decades as do mylar caps. The coils and resistors should last for virtually forever.
So there are plenty of 50-70 year old speakers that still perform as new, but others from the 70s, 80s, and 90s that will need surround and cap replacement. If the speakers were simply left in storage, they can usually be gone through and be made as good as new. If they were played in a deteriorated state, they can be permanently ruined.