Yes , that is true . It happened sometime back with one of my friend ,do not ask me the name , he had been told before joining the company , but did not get paid because he is only having the oral proof . So , better to have a written proof.
I'd advise you to seek a lawyer. To begin with having to pay to leave a company sounds pretty sketchy and is probably illegal in most if not all states. (You didn't specificy a location so I don't know which state you work in, although since you're posting on a US job baord and didn't list a location I presume a US state or protectorate.)
I've seen something that may equate in other countries.
Here in the USA, I am in an "at will" state - I can leave at any time without giving notice without ramifications. Of course the downside is that my employer can sack me at any time without giving notice without ramifications.
In many other countries there is a period for which notice must be given by either party. In some cases it can be as short as the pay period (so if you get paid every 2 weeks, then the notice period is 2 weeks). In London I was on a 3 month notice period.
What that means effectively is that should I be working somewhere where my contract states that there is a notice period, then if I should leave without giving notice, then I owe the company the wages for that notice period (so if I had left London without notice then I would have owed 3 months pay to the company). Conversely, if they were to sack me without notice then they would owe me the salary for that notice period.
In these cases, it is not always the case that an employee must pay to leave a company - only if they choose to leave without giving notice.