My mom is current living with me 6 weeks, she fell at her assisted living. She wants to live with me I don’t know if I should let her? Help?

Along with Barb I cannot imagine how long basement placement would be OK in terms of stairs, in terms of forgetfulness and possibly negotiating them.
Only you can make this decision, but in your stead I could not do this. I would know my own limitations could not stretch to attempt this.
Whatever your decision it is not one that you cannot change in the future. If she leaves her assisted living make it clear to them that you are going to "try this" due to covid and other reasons but that you are very uncertain as to whether it will work or not. Make the same clear to your Mom as it may fail for any one of many reasons. Remember, your Mom will not become mentally or physically stronger. Carpets can cause falls and hard basement floors can make breaks in 94 year old bones almost a certainty.
I wish you the best whatever decision you make. You clearly are trying to get all aspects of this together.

What would the kitchen area be for? Is she able to cook even simple things for herself, get herself a hot drink, make a sandwich?

How long was she resident in the ALF before she fell?

If its ok with your husband Let her stay with you.
Use the money to make her a cozy little apartment in the basement. Have her up for lunch & dinner a few times a week. Interview for a caregiver to take her for walks and shopping. Ask your sibs to call regularly and get relatives to send cards.
Hopefully mom will be able to enjoy some of her final years.

How is that safe, to have your mom in the basement if she can't do stairs?

How would she get out in a fire if you and sitters were not home.

She is far, far safer in the AL.

Is her depression being treated by a geriatric psychiatrist or other well-qualified mental health professional?

This is a tough situation. Covid changed everything! I feel that you still have to look at the whole picture. Why doesn’t your mom like her assisted living facility?

Is there something in particular or is she fearful due to Covid? Has her facility been effected by Covid? Is it possible to place her in another facility that she is comfortable at? Or is she difficult to please?

Since you already know that you don’t really want to have your mom living with you I would be concerned that as time goes by you will grow to truly resent the situation and that wouldn’t be good for either of you.

I had my mom living with me for 15 years so trust me I completely understand the emotions that you are struggling with.

How dependent was she on the additional services provided by her assisted living facility? Unless you will have a ‘live in’ sitter, you will be helping her with what is needed. It is exhausting caring for an elderly parent.

Please don’t make this decision out of guilt. I sincerely wanted to have mom live in our home and it still did not work out. Oh, it wasn’t bad in the beginning and I felt good about it but as the years went by it became emotionally and physically difficult.

I am glad that you are reaching out at this stage. I didn’t know about this forum until I hit a burn out stage.

I thought the only way to show mom that I loved her was to have her living with me. That wasn’t true. I just didn’t know it.

Everything Grandma1954 said plus...are you prepared to revolve your life around her? That is what will happen. She wants to live with you because you will give her all the attention. Assisted living facilities do not have employees just there to fuss over the residents.

Did you always get what you wanted in your life? This is no different. Keep her through the end of Covid but then she must go back.

Agree with everything Grandma1954 pointed out. Please remember that she is in decline, meaning she will not stay at her current level of care for long. Also remember that your brothers are not obligated to be "assumed" into helping you -- just assume they will not ever. So, are you ok with that? At some point the amount of care you will need to hire for her will exceed what you're paying at a facility, and be much more work for you. I absolutely understand your inner conflict about having her return to AL. Have you researched to find out if your state has passed "essential caregiver" legislation so that you will be able to visit her daily in a facility? We now have this in MN as of June. This knowledge may make the decision "easier". I wish you all the best, and peace in your heart no matter what you decide.

No, do not have her live with you. A basement bedroom when she is prone to falls? Assisted living is the best option especially since she already has the space.

Check with the building department on requirements for kitchens in the basement. And no, you would not be able to use mom's money to make improvements to your home.

Is your basement set up to have a bedroom? Is there a legal way to get out of the basement, other than the stairs up into the house? Can rescue people get into the basement? (so a door or access window)
What will happen when she can not do the stairs any longer?
Is there a bathroom that is large enough that you can get equipment into it and have room to move around? By equipment that includes wheelchair, Sit-to-stand, Hoyer lift.
Can you handle her living with you for another 1, 2, 4, 5 years? No one knows how long
If you do this you can charge her rent and a portion of the utility costs as well as any other household expense. You can charge her for your caregiving as well as anyone that is hired comes from her assets. I would also, to make things easier hire caregivers from an agency rather than on your own. If you do hire on your own make sure it is "legal" and that taxes are taken out and income is reported. Also make sure your homeowners insurance covers employees.