I think the only time you might lose the handset would be if you have one of those contracts that includes a credit agreement for the handset, is this the case for either of you? What happens to the handset if you default should be included in the contract t&C's, so have a look there.
Also if you're applying for a DRO it's probably worth looking at the Moneysaving expert forum for this, as there's really knowledgeable people there, especially for advice about setting a sustainable budget.
For example the amount allowed for groceries in formal debt solutions is really quite generous as it needs to include a lot of small general sundries that people forget about like light bulbs, batteries etc and is likely to be quite a bit more than someone in unmanageable debt would often spend because by that stage they've often spent a few months reducing their grocery spend to try and keep up with debt repayments. I read about a poster on here who was allowed £400 pm for her and one teen.
forums.moneysavingexpert.com/categories/iva-dro
My advice would be to find out about this now, and possibly buy a new handset you can keep and then transfer to giff gaff or similar as you will be able to keep using that when in a DRO as it's not a credit agreement, you just pay monthly by debit card. If you're planning to go into a DRO, you might as well stop paying your debts anyway so hopefully you can find the money this way to get a phone. Look at CEX or similar, or the Motorola G range.
I have a G7 which was £100 and despite being nearly 2 years old and bypassed by a couple of models, it's still really good
Also have you transferred your bank account to one you don't owe any money to so your banking facilities won't be interrupted after you have your DRO?
Hopefully you've both 'prepared' properly for the DRO to be as smooth as possible but the MSE link should give information about the kinds of things you need to think about.