If I am receiving alimony for 4 years... am I able to receive unemployment income if I do not have a job at the end of the 4 years after paying taxes on the alimony.

You receive unemployment when you are laid off from a job, or in certain circumstances fired from a job. You apply and your state waits to hear from the employer. You won't be able to collect it from alimony ending, and you won't qualify based on any past work, because it's based on the last 15 months of employment.
Paying taxes on the alimony is not relevant.
Your title says social security. Can you explain further what your question is? Are you on disability, and wondering how benefits will be affected when alimony stops?