The owner's equity of a sole proprietorship will change only if the disposal of an asset causes a gain or loss to be reported on the income statement.
To illustrate this, let's assume that a truck that was used in the business is sold for $5,000. If the truck had a cost of $40,000 and accumulated depreciation of $35,000 there will be no gain or loss reported on the income statement. The reason is the $5,000 received is equal to the $5,000 of book value that is being removed from the balance sheet. With no gain or loss on the disposal, the owner's equity is unchanged.
On the other hand, if the same truck is sold for $3,000 there will be a $2,000 loss ($3,000 of cash received versus the $5,000 of book value removed) reported on the income statement. When the account Loss on Disposal of Assets is closed, the owner's capital account will be reduced by the $2,000 loss.