That is interesting that you have a contract that, in effect, is an "at will" contract.
KS is an "at will" state for employment law matters. As an "at will" employee, the employer can fire you for no reason at all. Or they can fire you for "cause" (if you do something in violation of company policy
or the law). The one thing that they can not do is fire for a "bad reason".
That said, if they terminated your contract, but continue to allow you to work? In effect you remain "at will"
This is really very similar to a case where a landlord and tenant have a lease
and at the end of the lease, neither party does anything...the tenant continues to pay and the landlord accepts the rent.
Your case is similar to that...since you continue (for over a month) to work, the landlord is obliged to pay.
So you are truly now an "at will" employee.
You can be terminated at any time, for any reason...but interestingly, you can not now be terminated for a "bad reason". A bad reason would be if they fired you based on your race, your gender, your religion, your age (if your over 40), disability, or marital status.
But to answer the question, yes...you can be terminated at will, with no notice.