When you buy a share of a public company, the share lives in your brokerage account in your name (or in street name on your behalf). When you buy on VeldenStake, your position is recorded in the VeldenStake ledger as a fractional claim on the company's common shares, identified by your account and the company's CUSIP-equivalent identifier. From your perspective: you own 0.32 of a SpaceX share. From VeldenStake's: it has recorded a $250.40 liability denominated in SpaceX shares, against an equivalent reserve held in custody.
Settlement happens on the same tick as the order. The cash leg debits your VeldenStake cash balance; the position leg credits your holdings; an audit row is written; an email confirmation is queued. There is no T+2, no broker-of-record handoff, no clearing house in the middle.
Your position is then held until the company goes public. There is no sell-back and no secondary market — pre-IPO shares are illiquid by nature, and the only liquidity before then is withdrawing cash you haven't invested. When the company IPOs, your position settles at the IPO price, and you choose to take it as cash or have the shares delivered to you.