If you have no income of any kind there is no reason or need to file a tax return, with or without dependents.
To be eligible for any kind of tax credit you must have some type of taxable income. To be eligible for a tax refund you must have taxes withheld from taxable income.
How were you and your children supported? Were you claimed as someone else's dependent? If someone else claimed you as a dependent, then you cannot claim dependents of your own, nor can you receive a stimulus check. What income--if any--did you have? if you had Social Security or some kind of public assistance, you might be eligible for a stimulus check, but without income earned from working, you are not eligible for any of the child-related credits like earned income credit, child tax credit or the childcare credit on an income tax return. However, dependents do not receive stimulus money-- so if someone else claimed you, you will not be eligible for the EIP (stimulus) payment.
We might need to clarify what year you are asking about. The tax returns everyone has been filing recently are for 2019--the tax year that ended on December 31, 2019. Next year in 2021 people will be preparing and filing tax returns for 2020. If you are receiving unemployment compensation in 2020, that is taxable income that you can enter on a 2020 tax return. It will not make you eligible for any of the child-related credits, but may make it easier for you to get the credit for EIP for yourself and the children.