Err I think I meant preferred shares? FOO buys in at $X valuation. If a liquidity event happens that doesn't meet price target $Y, FOO gets paid out before the previous holders altogether or at some higher percentage.
Yes, investors with preferred stock usually get their money back first. Sometimes they get a multiple, but that's considered overreaching nowadays and the more promising startups never have to agree to that.
I suppose that is implicitly a target valuation in a sense. But no one views it as a target, because it only matters if things go badly.