I preface these comments by saying that I am no expert in insolvency law, as I have no personal or legal experience of this area. What follows is tentative, and may well be worth running past those with more experience, such as those in the relevant part of the MoneySavingExpert forums.
There is a need to be careful here, as doing a deal with Sky risks being construed as preferring one creditor over another. Preferences created within a certain time frame before going bankrupt (I think it's six months) can be set aside by the court.
However, there is an argument that a phone line and a basic Internet package is an essential of life that would likely cost more to reinstate in bankruptcy (if it is possible at all, considering the lack of creditworthiness) than to preserve now. This arguably heads off the argument that a preference was created in detriment to other creditors. I would also argue that the risks of a creditor complaining about a few months of phone and broadband costs are low compared to the size of what must be substantial debts to be contemplating bankruptcy.
As such, if the person can get the money together to pay off the broadband and phone line arrears on top of other essential expenditure and getting together the fee for bankruptcy, it may be worth offering Sky the broadband and phone line arrears in return for resumption of broadband and phone line service.
Sky probably will try to press for clearance of all arrears, but it is worth stressing that this arrangement leaves them better off than if the entire debt falls into the bankruptcy, as it guarantees Sky recovery of all of the non-TV part of the debt in order to restore essential services. I would stress that with bankruptcy pending, funds are not available to clear the TV debt, that there is no intention to resume multi-channel TV service with Sky or any other provider and that clearing debt relating to non-essential services risks creating a preference that cannot be justified.
It might also be worth the person volunteering for an outgoing call ban if they have another way of making calls or asking for a ban on out-of-bundle calls if they feel the need for a reasonable call bundle. This, together with offering to pre-pay a month if funds allow, would limit Sky's credit risk in restoring service.