Apply for SNAP anyway. The requirements are purposefully hard to understand because that creates a barrier that discourages people from applying, which saves money. If you get denied, whatever, but if you don't apply you won't even see what you are eligible for. And there are several ways to meet the work requirements beyond just working a regular job. Having an active SNAP case, even if your allotment is $0 a month, will give you an active case number which can be used for income verification for other programs like free phone service.

For disability, count in getting denied the first time. Generally that's standard practice, and you may need more than one appeal, but if your wife is unable to work she will eventually get approval as long as she keeps her doctor's appointments and gets everything documented. Don't mess around and smile or say something like "fine" if one of those doctors asks how you're doing--they will write it down and it will go in your file which will look like the doctor thinks you are without pain. There is also Vocational Rehabilitation which helps people with disabilities get jobs and accommodations so they can do their job comfortably. Good luck.

But there are food banks or pantries available. Google your area and see what comes up.

What did your wife previously do for work? If it's just being wheelchair-bound, most desk jobs should be possible (although obviously unfairly harder to get/keep than if she were able-bodied).

Have her doctor write that her medical conditions affect her ability to aquire and maintain employment.

SSI, if that is what you're looking into, has a process for people who don't have verifying documents. Just keep appealing and you should be able to get to someone who can "assess" you. And, when you do applications and interviews, they don't wanna know how you usually do, they wanna know how you are on your WORST DAYS. SSI is also for people who both cannot work at all, or cannot work to their full potential due to disability.

>Looked into the requirements but we don’t think we qualify.

Just because you think you do not qualify does not mean that you do not actually qualify. You will never know unless you actually apply.

Hit up google and see if there are any groups in your area/state that you can talk to about your options to get help with your current situation. There may be groups (or even subreddits here) that can guide you through the application process for welfare benefits/SNAP/etc to increase your chances of qualifying or there may even be state programs that can help you out (e.g. help for covering medical bills/prescriptions, help with rent and/or bills, etc). You might be able to find groups who can provide you with food hampers to help cut down the cost of your food bills.

One of the biggest issues I often see with getting help when you are in financial distress is actually finding the services that are out there to help you in those times of need. This is where the groups that I mention above can really help you out.