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Difficult with collections, especially if they're large amounts on which a judgment can be filed.
If they're small, then BofA, Wells, and US Bank all have secured cards, but I think they'd reject with outstanding unpaid COs. Cap One secured might be the best option in this scenario.
Any bank that would grant your partner a secured card is a good bank. A BofA's card will secure after one year, and offers cashback rewards, but gets reported as a secured card. A Capital One card probably will not secure, does not offer rewards, but gets reported as a regular card.