Oil (rather olive oil) is a metaphor or "symbol" of the Holy Spirit. This is seen in several OT scriptures (Exo.30:30, Lev. 4:3-5, Num.3:3, 1 Sam.16:13, Ps. 2:2, Isa.61:1, Zech.4:1-6) as well as in the NT (Matt.25:1-13; Acts 1:8; 10:38, Gal.5:16; Eph. 5:17-18) etc.
So, if someone has no oil...