According to LegalZoom, if the sons must create a new business since a sole proprietorship is non-transferable. Once the original sole proprietor dies and the business is transferred, all of the business’s assets must still pass through probate. The sons might have to settle the outstanding debts to protect the business’s assets from creditor claims. Settling debts and restarting the business may require significant amounts of money. Ultimately, the sons need to create a new business then transfer all of the former proprietorship’s assets into that organization.

http://info.legalzoom.com/sole-proprietorship-someone-dies-23863.html