The provider has a legitimate interest in the data subjects data, and therefore they can override the right of deletion.
See this example from the UK's Information Commissioners Office:
A finance company is unable to locate a customer who has stopped making payments under a hire purchase agreement. The customer has moved house without notifying the finance company of their new address. The finance company wants to engage a debt collection agency to find the customer and seek repayment of the debt. It wants to disclose the customer’s personal data to the agency for this purpose.
The finance company has a legitimate interest in recovering the debt it is owed and in order to achieve this purpose it is necessary for them to use a debt collection agency to track down the customer for payment owed.
The finance company considers the balancing test and concludes that it is reasonable for its customers to expect that they will take steps to seek payment of outstanding debts. It is clear that the interests of the customer are likely to differ from those of the finance company in this situation, as it may suit the customer to evade paying their outstanding debt.
However, the legitimate interest in passing the personal data to a debt collection agency in these circumstances would not be overridden by the interests of the customer. The balance would be in favour of the finance company.
Article 17 of the GDPR, the "Right to be forgotten", says this:
The data subject shall have the right to obtain from the controller the erasure of personal data concerning him or her without undue delay and the controller shall have the obligation to erase personal data without undue delay where one of the following grounds applies:
A) the personal data are no longer necessary in relation to the purposes for which they were collected or otherwise processed;
B) the data subject withdraws consent on which the processing is based according to point (a) of Article 6(1), or point (a) of Article 9(2), and where there is no other legal ground for the processing;
C) the data subject objects to the processing pursuant to Article 21(1) and there are no overriding legitimate grounds for the processing, or the data subject objects to the processing pursuant to Article 21(2);
In your example, it's obvious that the personal data is still necessary for performance of the contract (Art 6(1)(b)) such as collecting payment, or for fulfilling legal obligations (Art 6(1)(c), Art 17(3)(b)) such as the obligation to keep financial records. Thus, there continues to be a legal basis for processing/keeping the data and rejecting the erasure request in whole or in part.
Things are slightly different when the legal basis for this processing was consent (Art 6(1)(a)) or a legitimate interest (Art 6(1)(f)). Consent can always be withdrawn, but this kind of data collection is not typically based on consent. You can sometimes object to processing under a legitimate interest (see Art 21) but that doesn't work when the data controller has overriding legitimate grounds to continue processing. Such overriding grounds might be the legitimate interest to pursue the debt, and Art 21(1) and Art 17(3)(e) explicitly call out the “establishment, exercise or defence of legal claims” as overriding grounds.
So that covers requests under A, B and C.
Things like legal basis and erasure/objection must be analyzed on a per-purpose basis, so it is possible that you could get a partial erasure, such as erasing information that's only necessary for marketing (compare also objection per Art 21(2)).
But its quite clear to me that a data subject cannot get out of paying a bill by using the GDPR.
