As a customer service representative who works with Emblem Card customers everyday, I would have to say that the only problem with the card is that people don't read the policies.
I can honestly say, yes, this is a legitimate company. It is up to the cardholders to keep up with their monthly minimum payments and then we will keep reporting to the credit bureaus. The credit limits are small, but many people love this because they have had issues in the past paying off large amounts of debt. Plus, paying off that smaller amount monthly shows well on your credit score.
The only way to get this card is to get an offer from Jefferson Capital themselves. They obtain old debts and send offers for the Fresh Start Solutions Program in which you make a few payments towards your debt depending on the amount of the debt, and then they will send out your Emblem Card. It's pretty simple and I personally do not have a credit card at all, but as long as you read the the policies that you are sent with the card, you should be just fine