It is an interesting thought to play around with - but probably not. If a company is allowed to frame firings they would use mild language and try not to refer to the situation at all ('the business was restructured', 'redundancy', 'layoff'). If the firing was for-cause the language gets a bit stronger ('terminated' for example would indicate that the person had done something that scared a team of lawyers or was otherwise egregious).

Firing is a slang term that would tend to be used by an unsympathetic press. The slang equivalent would be quit which has a similar strength.