You did not work for this company, you worked for the temporary agency that placed you on your worksite. When you file for unemployment, you will find that your unemployment taxes have been paid in on you as an employee of the temporary service, and they are the ones who will be contacted as the separating employer. Since your worksite has decided they do not want you there anymore, whether or not you are approved for benefits will have a lot to do with whether they have another assignment for you, whether or not you accept such an assignment, whether the reason you are terminated from your last assignment was due to your own fault, and frankly, refusing to be put on full time, refusing to accept "other tasks that were within your means" it sounds like you generally managed to get put out of work due to your own good efforts. It doesn't sound like there's even the faintest possibility of this situation being a wrongful termination, and not too terribly great an opportunity to qualify for unemployment insurance. But by all means, go on and file a claim for benefits.