In practical situations such as hostage rescue, earthquake and other similar events, the ultra-wideband (UWB) life-detection radar echo response from the respiration motion of the trapped person is always quasi-/non-periodic in respiration frequency or very weak in respiration amplitude, which can be called quasi-static vital sign. Although it is an extremely difficult task, considering the economic cost, the detection ability of the traditional UWB life-detection radars with only a pair of transceiver antennas is desired to be enhanced for locating the quasi-static trapped human being. This article proposes two different detection methods for quasi-static trapped human beings through the single/multiple observation points, which corresponds to the single-/multi-station radar operating mode, respectively. Proof-of-principle experiments were carried out by our designed radar prototypes, validating the effectiveness of the proposed methods.