S.,
I am so sorry for your loss. I am a Realtor and owner of several rental properties. I always try to do what is fair for all in situations like your's. We recently had a similar situation. Our tenant wrote me (e-mailed) that her health had deteriorated so she couldn't work and that it was necessary to move back home with here parents with her two children. I let her know that if she would leave it clean and ready to rent that we would try to find a replacement for her. As long as there was no loss to us, we would be willing to release her. We had actually rented it to her for $100/mo. less than the previous tenant. We were able to find a new tenant, but it took a month. Therefore, we used her deposit as that month's rent and leased it for $100 more per month. We were actually out a little, changing locks, having carpet cleaned, etc. But, we were blessed with a tenant who was actually better qualified than she was.
In your case, you both signed the lease. What the management company should be willing to be fair by allowing you out of the lease if they have a replacement tenant. I like the suggestion that you put an add in the local paper and find a replacement tenant for them to approve and take over your lease. I don't recommend going to court against them because I have found that large management companies are very "friendly" with the judge and you will probably lose. However, if you truly can't afford it, you should move as soon as possible. Leave it as clean as you found it. Have a witness and take pictures. They will have a better chance of replacing you sooner if it is ready to move in to. However, if they have several vacancies, they will lease the other ones first because they alresdy have you on the hook. If you have a potential replacement tenant, you can control that part of it. The replacement tenant must be equivalent to you and your husband's qualifications at the beginning of the lease as in income and credit. It might help to show them proof that your income is not sufficient to handle the rent after your Husband's death, if that is the truth. It is true that the actual manager of the complex may not have the authority to release you from your agreement, so it would be better to communicate with their supervisor or owner. As others have said, in either case, it is better not to stay if you can't pay the rent.
My Daughter was in an apartment (in Kerrville) that flooded 3 times. Her fiance' had been there 3-1/2 years. They had just signed a 6-month renewal. After the 3rd flood, I found them a cute mobile home to buy. The apartment was unlivable for 21 days. The complex sued them for NEW replacement of the carpet and the remainder of the lease, and won. I was there and couldn't believe that a judge wouldn't listen to the fact that the carpet was used for 3-1/2 years, flooded 3 times, etc. I explained that the normal life expectancy of rental carpet was about 7 years. They lived on it for 3-1/2 years, equaling half of the life and flooding 3 times was the other half. It didn't matter. She (the judge) gave them a judgement for 100% cost to replace it and the remainder (5 months) of the rent. I could tell that the judge was "in the management company's pocket". That is the only explanation for why she didn't listen to reason. They didn't actually file the judgement, though and it didn't affect my daughter's credit.
Bless you. Pray for favor in your dealings with the management company before you pursue it. If your lease has the "Reletting Fee" verbage in it, most TAA forms call for 85% of a month's rent to be paid as a reletting charge. This amount is in addition to the security deposit. If you leave the unit clean and ready to rent, they should settle for just your security deposit if it covers any lost rent until they re-rent your unit. Whatever you do, make sure you have it in writing so you can document your effort to be responsible. If you do your best to be fair, that is all you can do. Even if it doesn't work out, you have the right to put up to 100 words on your credit report explaining your side. Any reasonable person would not hold it against you for having to break a lease because your husband passed away.