This is a slightly more complicated topic (i.e. it's complicated by whether or not manual recovery is possible and by whether or not carrying on makes it worse), but in general, the worst thing you can do if you encounter an error in the software that supervises a process is to bail out and leave the process unsupervised. A chemical reaction, for example, is happy to carry on whether or not computers are watching.

There are plenty of situations when automated or manual recovery isn't possible and/or where carrying on with a potentially damaged system can make things worse. In practice, you solve this sort of problem via other design solutions, like redundancy. If you think that a critical system needs to keep running, but you also think that some errors will have to be handled by shutting it down, then you make it redundant.

Airplane FBW systems are a good example (caveat: I don't do airplanes, I do medical stuff -- I might be wrong about the practical details of this but I think it gets the point across). If the ELAC (elevator and aileron computer) runs into a condition it doesn't know how to handle, there's a good chance it will make things worse if you keep going. But you also don't want your mitigation to be "just halt the damn ELAC", you still want to have control over the elevator and the ailerons. That's why there are several ELACs.

More to the point: if something has to keep happening, no matter what, then you design the computing system and the firmware around it so that it keeps happening.

> At design time you better figure out what all the error cases are

Not being able to figure out what all the error cases are has been an unfortunate component of systems engineering for decades now. The Wright brothers would have probably been able to account for all the failure modes in their flight control systems, but today, you are likely to miss some of the failure modes of a CPU that executes nothing but a NOP and a jump back to that NOP.

With the exception of simple and special-purpose systems, built without any programmable logic whatsoever, it's unlikely that you'll be able to figure out what all the error cases are. (There's something to be said here about OISC and whatnot...)

That's not to say it's OK to build systems that blindly steamroll over errors -- just that you have to build them so that they can deal with errors that you have not foreseen at design. You will run into that sort of error sooner or later, we are all failible.

Edit: as for assertions, performance may be a factor, but that's not why you want to turn them off in production builds for embedded systems. (Although, IMHO, this isn't the right approach for embedded systems at all, but I've seen it used).

First of all, you turn them off because, presumably, they make your system deviate from the spec (i.e. the system ends up handling some cases differently in the production build vs. the debug build, and hopefully the one in the production build is the one you want).

Second, you turn them off because they can introduce undefined behaviour in your system. For example, if a peripheral gives you an incomplete or malformed packet in response to a command, or fails to answer altogether, you may want to abort with a stack trace in a development build. But what you really want to do IRL is probably to check and reset that peripheral, because for all you know it may be stuck and giving haphazard commands to an actuator.

IMHO, assertions are only a partial answer to the problem you really want to solve -- obtaining useful data (e.g. stack traces) in response to error conditions. You can generally log the useful data in addition to actually handling the error correctly. Development and production builds should differ as little as possible -- ideally not at all. Handling potentially critical errors in different ways certainly doesn't count as differing as little as possible.