It depends on the nature of the agreement or lack thereof
Independance can be radical or moderate, gradual or sudden, negotiated(brexit) or forced(ukraine), and the new country may inherit debts in it's regional programs, it may have assets frozen, trade barriers...
You can see from the Brexit negotiations that even a constitutionally predicted seperation are centered over the extent of the shared debt, versus the customs and trade agreements.
When Scotland voted to leave the UK, one of the biggest negotiations would have been over national Gas and Oil mining operations and rights in Scotland.
Honestly the question is a thesis query, and more precision or knowledge of the topic would have shown that you thought about it and have some further thoughts on the topic, to make it less vague to honestly respond to.