Use escrow. Sign the agreement, place the cash in escrow with release conditioned on visa issuance, and apply. Closing outright before the visa exposes the couple to owning a U.S. business they cannot run; waiting to sign leaves nothing committed.
Escrow lets you commit without closing
E-2 requires that the funds be irrevocably committed before the application, but recognizes a commitment held in escrow whose sole condition is the issuance of the visa. That structure fits a purchase of an operating business well. The couple sign the purchase agreement, fund the escrow with the cash and home-secured portion, document the seller note separately, and apply at a U.S.
consulate. If the visa issues, escrow releases and closing follows; if it is refused, the funds return and the agreement unwinds under its own terms. Negotiate the escrow and the unwind clause with the seller at the outset, since a seller who wants to retire may prefer a firm date.
Canadians apply for the E-2 visa at a consulate, so the interview appointment sets the timeline; check current wait times before promising the seller a closing date. After issuance, admission is for two years at a time with renewals available as long as the business continues to qualify.