There is nothing wrong to "ignore" errors like out-of-memory, as long as you know the consequences. Terminating the application on fatal errors is part of error handling. That's fine.
But you should never ever ignore(!) errors, hoping for the best (and I think try-catch encourages this, so I don't like it).
That's the mess I'm dealing with today. Lots of secret suppression on dozens of cases. Once we started logging and stopped seeing obsolete responses, the data loses started coming in. That's raising a lot of concern now
Management (no error checking): everything looks good !
Management (error checking): our developers SUCK ! They constantly get close to losing data or insist on the database having this "correctness" technobabbly thing. Idiots.
But you should never ever ignore(!) errors, hoping for the best (and I think try-catch encourages this, so I don't like it).