We performed a comprehensive stacking analysis on ∼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_⊙) have drastically different IR and radio properties depending on their 24 μm emission strength. The fraction of QG candidates with strong 24 μm emission (equivalent to inferred star formation rates SFR_24≥ 100 M_⊙ y^-1, hereafter “IR-bright”) increases with redshift and peaks at 15%, and their stacked MIPS 24 μm, 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 μm individually (i.e., SFR24 < 100 M_⊙ yr^‑1, hereafter “IR-faint”). Their low dust-obscured SFRs derived from Herschel stacking (SFRH ≲ 3, 15, 50 M_⊙ yr^‑1 out to z ∼ 1, 2, 3) are >2.5– 12.5× 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 LIR derived from stacking Herschel and 24 μm indicates that IR-faint QGs have dust SEDs that are different from those of SFGs. For the most massive (M_* 10^11 M_⊙) IR-faint QGs at z < 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.