If you reached an agreement with the other vendor and signed a contract, you could easily be sued for breach of contract if you fail to pay for the contracted service. Even if the contract wasn't signed but you had an agreement, you can be sued. If there is no agreement and you're in the negotiations phase, a suit is possible based on promissory estoppel. There are other forms of estoppel, but it's hard to see how they could possibly apply in this situation.
Normally you would have the right to ignore those guys, but you could be legally prevented from making that claim in court under that doctrine of estoppel. They would have to establish that there was a promise, and they relied on that promise to their detriment (for example, hired extra staff, rented a new building). This article looks at numerous cases of promissory estoppel cases.
Anyone can file a lawsuit. The process is spelled out for one jurisdiction and set of circumstances here. The suit might be easily dismissed for many reasons – the point is, anyone can file the papers. This page gives a general overview of filing suit, and for your jurisdiction you can look up the specific rules and probably find examples of complaints that were filed.
Failure to say anything to the other party does not prevent them from filing a suit. If you conclude a contract with another vendor but string the outside guys along, you could in fact be sued successfully (they will have been harmed, in investing further resources to get the contract, and you misled them into thinking that they count get the business: Aspex v. Clariti).