You don't say if this is a UK company, but if it is, the UK Inland Revenue will confirm the dates you were employed at a company. You can get them to issue you a letter confirming all your employment dates, or dates at a specific company. Of course, if a company has gone out of business, I can't see any other way of doing it, except by going to the HMRC.
I don't know what the legal position is, but a company should be able to confirm your employment dates, but may refuse to answer any specific questions. This can be quite common with today's litigious society.