The quick answer
If the business is a solvent partnership then it will be dissolved by agreement between the relevant parties in accordance with a partnership agreement. If the business partnership is insolvent and cannot pay its debt then it will go into Liquidation, Administration or a Partnership Voluntary Arrangement (“PVA”).
In more detail
There are two types of partnership. The first is a partnership where all of the partners are jointly and severally liable for the debts. The other is an LLP where there is limited liability.
In the case of an insolvent partnership needing dissolution, the usual route is Liquidation. In more urgent situations Partnership Administration can be used as it is a faster option. It is also very useful where a business can be rescued as it stops all legal action, such as the bank, appointing a receiver.
For a normal (non LLP) partnership, the partners are all jointly liable for the debts not paid for by the partnership assets. This can have serious implications for the individual partners which might mean that a PVA is a better route and even possibly Individual Voluntary Arrangements for the partners.