Liability differs fundamentally between the two forms.
In a general partnership: partners are personally and jointly liable for the company's obligations in all their assets, and any agreement to the contrary is void (art. 33). Company creditors may recover from the company's assets and also from any partner's personal assets, but execution against a partner's personal assets is only allowed after notifying the company to pay and fifteen days passing without payment (art. 53). A new partner who joins is liable for obligations arising after joining, and a withdrawing partner remains liable for obligations that arose before his withdrawal was registered (art. 54).
In a single-person company: the owner is liable for its obligations only up to the capital allocated to the company (art. 85). However, he is liable in his personal assets if he liquidates it in bad faith or stops its activity prematurely, or if it is proven he did not separate his own finances from the company's in a way that harms good-faith third parties (art. 90).
This is general legal information, not legal advice. For advice on your specific situation, consult a lawyer licensed in Kuwait.