When you are a low income family and are unable to afford diapers or you're suddenly faced with a job loss or income loss and have kids in diapers and need diapers for them you can usually get free diapers by checking around to see if you have a diaper bank around your area.
Some places have diaper banks which are like food banks but instead they give out free diapers to parents who need them for their kids.
You just have to prove your income and it's a good idea to bring your baby or toddler along with you to get the diapers because it proves that you have a baby or kid that needs diapers.
Then you can usually get a month or weeks supply of free diapers that way.
You can also ask a local church and they may be able to help you get diapers for your baby or toddler.
Another option is to check on Craigslist for free diapers as some people will offer up free baby or toddler diapers that their child has outgrown or when the child has potty trained they will give the diapers away free or even sell them to you at a low cost.
I've gotten cheap baby diapers through Craigslist and even free diapers for my kids through that.
Another option is to buy some cloth diapers and cloth diaper your baby or toddler if you cannot afford disposable diapers.