We performed a comprehensive stacking analysis on similar to 14,200 quiescent galaxy (QG) candidates at z = 0-3 across mid-, far-infrared (MIR and FIR), and radio wavelengths. Identified via their rest-frame NUV - r and r - J colors, the QG candidates (M-* = 10(9.8-12.2) M-circle dot) have drastically different IR and radio properties depending on their 24 mu m emission strength. The fraction of QG candidates with strong 24 mu m emission (equivalent to inferred star formation rates SFR24 \textgreater= 100 M-circle dot yr(-1), hereafter “IR-bright”) increases with redshift and peaks at 15%, and their stacked MIPS 24 mu m, Herschel (PACS and SPIRE) and VLA emissions are consistent with being star-forming galaxies (SFGs). In contrast, the majority of QG candidates are faint or undetected at 24 mu m individually (i.e., SFR24 \textless 100 M-circle dot yr(-1), hereafter “IR-faint”). Their low dust-obscured SFRs derived from Herschel stacking (SFRH less than or similar to 3, 15, 50 M-circle dot yr(-1) out to z similar to 1, 2, 3) are \textgreater 2.5-12.5x lower than compared to SFGs. This is consistent with the quiescence, as expected from their low unobscured SFRs, as inferred from modeling their ultraviolet-to-NIR photometry. The discrepancy between the L-IR derived from stacking Herschel and 24 mu m indicates that IR-faint QGs have dust SEDs that are different from those of SFGs. For the most massive (M-star \textgreater= 10(11) M-circle dot) IR-faint QGs at z \textless 1.5, the stacked 1.4 GHz emission is in excess of that expected from other SFR indicators, suggesting a widespread presence of low-luminosity active galactic nuclei. Our results reaffirm the existence of a significant population of QGs out to z. =. 3, thus corroborating the need to quench star formation in galaxies at early epochs.