New equity comes with a new CUSIP, often a new ticker-symbol, and a share count set by the plan. Owning the old shares gives you no claim on it unless the plan-of-reorganization explicitly grants old holders shares or warrants, which is the exception rather than the rule.
New equity typically trades thinly at first because its owners are credit funds that did not choose to be equity investors, and because the company often lists on the over-the-counter market before applying for an exchange listing.
Example: 100M new shares are issued, 95M to former noteholders and 5M as a management incentive pool. Old common, 340M shares, is cancelled. Anyone who bought old shares at $0.18 receives nothing from the new stock's $14 debut.
Related: chapter-11, plan-of-reorganization, absolute-priority-rule, ticker-symbol, uplisting