on what basis an independent 1099 contractor can sue an s-corporation without a written contract.

It appears that the contractor is claiming that the company breached its (I say "its" because I assume that the "company" is a corporation, llc, or other legal entity) contract with him, but I can't tell from your question what term he believes was breached.  In most cases, a verbal contract is as valid and binding as a written one (although much more difficult to prove, obviously), and, from the information you've provided, it doesn't appear that this contract was one which needed to be in writing to be enforceable (some examples of which are agreements to sell real estate, agreements which can't possibly be fully performed within one year, etc.)  You should be careful to preserve all documents relevant to your dealings with the contractor and performance of the contract, and that you make no admissions in any correspondence you have with him, even by silence.  Thus, for example, if the contractor emails you to the effect that "we had an agreement that you would pay me $x for every week the employees I recruited worked for your company", and that was not your agreement, you should make sure to respond that "that was not part of our agreement."  In fact, you may want to make a blanket disclaimer on any response to him, along the lines of "we don't agree with any of the assertions you've made in your emails, but for the sake of trying to resolve this dispute ...., etc."  JDepending on how serious he seems about suing, and how much money is involved, you may want to retain an attorney and refer all communications to him/her.