Can a vendor take-back note convert into equity in my company if I default?

Only if the buyer and seller specifically negotiate and document that feature — a standard vendor take-back note is simply a debt instrument with whatever security and default remedies were negotiated for it, and does not automatically convert into shares of the buyer's corporation just because a default occurs. Equity conversion on default is a distinct, additional feature that needs to be expressly built into the note or a separate agreement at the time the deal is structured.

If a seller wants the option to convert unpaid amounts into an equity stake in the buyer's corporation on default, this raises its own set of complexities beyond an ordinary debt-and-security arrangement, including how the shares being issued would be valued at the time of conversion, how that would interact with any existing shareholder agreement, and whether securities law considerations apply to issuing shares in that way. These issues are far better worked out carefully during the original deal structuring, with proper legal and accounting input, than improvised or negotiated for the first time after an actual default has already occurred.