No. If you do not have an employment contract, your employer can change the terms of your employment, including compensation, at any time as long as it is not enforced retroactively.
Under some circumstances, a reduction in compensation can be considered "good cause" for quitting and put a worker in a rare category of individuals who are able to quit their jobs and still collect unemployment. Without more information, though, no one would be able to tell you whether or not you may be in this category.
This answer is provided for guidance only. DO NOT rely on it as legal advice. We DO NOT have an attorney-client relationship. You should contact an attorney in your area for a one-on-one consultation before pursuing any action or making any decisions.
It need not be in writing. However, you may be entitled to unemployment. Also, if the reason for the reduction in pay was discriminatory, you may have a claim. If you have questions, you should contact an experienced employment attorney. Many of us, myself included, will provide a free consultation.
This answer is provided for informational purposes only and should not be relied on as legal advice. You should be aware that no attorney-client relationship is established through this answer and none will be established without a personal consultation and the signing of an engagement agreement.
If you are not under and employment contract, then your employer can change the terms of your employment. Due to the drastic nature of the wage reduction, you should look into the possibility that you qualify for unemployment compensation.
You are clearly eligible for unemployment and can continue to work, if you are working less than 40 hours. However, the actually amount may be $0. You should contact the local office and get your weekly benefit amount. You can make 1/2 of that amount per week. For each dollar over the 1/2 you make, IDES takes away a dollar. So, if your wba is $300, and you make $150 a week, you get the full $450. If you make $250 a week, you only get from IDES $200. I was a judge at IDES, so this is ready for me to figure out. If you have questions call me at 331-222-9529.