Lewis & Short

stătūlīber (also separate, stătū lī-ber), bĕri, m. [prob. instead of statuto liber; v. infra], a slave to whom liberty is granted under a certain condition or from a certain time, generally by testament: statuliber est qui statutam et destinatam in tempus vel condicionem libertatem habet, Dig. 40, 7, 1: qui sub condicione testamento liber esse jussus est, statu liber appellatur, Ulp. Fragm. 2, 1; cf. Titin. 2 passim: statuliber est qui testamento certā condicione propositā jubetur esse liber, Fest. s. v. statuliber, p. 249 L.: statuliberi, id est ejus servi quo testamento sub aliquā condicione liber esse jussus est, quem constat interea heredis servum esse, Gai. Inst. 2, 200: cum statuliber sub condicione legatus est, et pendente condicione legati condicio statutae libertatis deficit, legatum utile fit; nam, sicut statuta libertas tunc perimit legatum cum vires accipit, ita, etc., Dig. 30, 1, 81, § 9; cf. ib. 33, 5, 9; 30, 1, 44, § 8; and the whole title of the Dig. 40, 7, De statuliberis.
The word perhaps occurred in the XII. Tables: sub hac condicione liber esse jussusad libertatem perveniet: idque lex duodecim tabularum jubet, Ulp. Fragm. 2, 4.