And if it does, then the business operates a 'first-refusal' policy. In cases where the business has decided to utilise the side-project, this is normally combined with financial compensation in some form (a salary raise, a bonus, something like that).
FYI, I'm in the UK (midlands). I think this is quite a liberal approach compared to most. But it seems to motivate staff to think outside the box in the interests of the business.