This hasn't happened yet, I see. When it does, your husband will immediately sign up on his unemployment insurance. This will take several weeks and will be quite a lot less than he was making, but it is some money coming in. He may if this is a plant closing, receive some severance benefits. Diligent job searches for both of you should be on the plans, shared child care arrangments for the both of you. If he is not working and you find a job, even a part time job, he can do the child care.
The man (your landlord) doesn't care. He is not obligated to care. Unless you have some form of subsidized housing, he can demand payment and that you honor your lease. He doesn't have to cut you slack. However, since you do have a month, at least, begin looking diligently for cheaper housing for yourselves, and for someone to sublease. "Not likely" does not mean impossible.
If your husband wants to stay in his "line of work" he may have to relocate to where the jobs in this line of work might be. Else he may realistically have to take something different that pays less, deal with the jobs that are available in your area.
Immediately take the children out of any expensive activities, private schools, lessons, programs. Begin a calculated program of economy before you run out of money, now before the job even ends. Set aside that next month's rent payment, (and utilities, it's big to have the lights and water on!) and then start figuring out how you can live otherwise, by cutting expenses. Cut off your cable. Have a yard sale. Sell anything you can on line. Consider trading down in automobiles. If you have creditors, see if you can re-negotiate your payment schedule. Student loans can be put on hold.Things may not be as desperate as they seem right now.
When people hear that they are losing their jobs, they do what is called "catastrophizing," which means your mind automatically jumps to the worst case scenario, which is of course that you can't pay your rent, can't find a sub-leasor and are dumped out on the street homeless with your kids going hungry. But realistically, this probably will not happen.
Terrible but true, this loss of jobs is happening all over the nation, has been for some time now. Being a stay at home mom is going to be tough to maintain when the wolf is at the door. But for a place that's big enough for three kids and two parents at $1045 a month isn't a real bad deal. Maybe you can swing it on less than you have been making.