Yes. In California, oral agreements are as enforceable as written ones, although oral ones are more difficult to prove. Your uncle has 2 years from the date of breach to sue. Without a contract in writing, he has to prove the contract and the breach through oral testimony, other witnesses to the deal, if there are any, the cancelled check payable to the "friend" and not to his business, confirming e-mails or other correspondence mentioning the deal, etc.
But: If the loan was to the company, and the company went bankrupt, and the company listed this debt in their bankruptcy petition, it would be discharged and your uncle couldn't sue. If the debt wasn't listed in the bankruptcy, then the debt wasn't discharged, and that would tend to prove that the debt was the friend's.
Disclaimer: Please note that this answer does not constitute legal advice, and should not be relied on, since each state has different laws, each situation is fact specific, and it is impossible to evaluate a legal problem without a comprehensive consultation and review of all the facts and documents at issue. This answer does not create an attorney-client relationship.
Before suing the "friend,' a lawyer would investigate the bankruptcy in order to determine whether the "business" was a separate entiry (like a corporation or LLC) or just a business name for the friend. The lawyer would also check to see if this is one of those rare cases in which creditors may receive payment from the bankruptcy.
Assuming that the corporation was a separate entity, you would be free to sue the friend. Limitations periods are shorter where no promissory note or written contract is involved. Perhaps as short as two years after the date the money was loaned.
Ms. Koslyn was correct in suggesting that if the debt is not listed in the bankruptcy filing, this may help the case against the friend, since that fact suggests that the friend regarded the loan as a personal obligation. However, even if the debt is listed you are not barred from pursuing the friend.
One note point on which I disagree with Ms. Koslyn; If the debtor in bankrutpcy is a corporation or LLC, no discharge will be obtained (corporations don't receive discharges in bankruptcy). The only significance of this is that once a corporate bankruptcy case is closed you don't have to worry about bankruptcy issues at all in pursuing this debt.