Let's take Java, for example (which does not have destructors and does have checked exceptions, which are actually somewhat tolerable):

DM>* Unchecked exceptions can actually happen basically anywhere. Not just inside functions. Because the Java specification raises exceptions for things like stack overflows, VM internal errors, allocation failure, etc. And Java also allocates everywhere.
DM>* By the way, implicit conversions from unboxed to boxed primitives are function calls in this context and can thus trigger these errors.