Some do, most don't. Saturn V could (and did several times) survive failure of a first-stage motor. STS (Shuttle) theoretically could survive an engine loss under some conditions. The Soviet N1 could well have survived a motor loss (it had 30 of them after all), had it flown and had they been able to control all those engines.
Historically, most rocket designs push the performance envelope so hard they have little or no margin. Much of this attitude is historical, government rockets mostly being descended from ICBMs. The other part is that the rocket equation severely penalizes extra weight, and the window between "robust" and "too heavy to fly" isn't all that large.
Historically, most rocket designs push the performance envelope so hard they have little or no margin. Much of this attitude is historical, government rockets mostly being descended from ICBMs. The other part is that the rocket equation severely penalizes extra weight, and the window between "robust" and "too heavy to fly" isn't all that large.