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Abstract: We investigate the nematic and loop-current-type orders that may arise as vestigial precursor phases in a model with an underlying pair-density wave (PDW) instability. We discuss how such a vestigial phase gives rise to a highly anisotropic stiffness for a coexisting single-component superconductor with low intrinsic stiffness, as is the case for the underdoped cuprate superconductors. Next, focusing on a regime with a mean-field PDW ground state with loop-current and nematic $xy$ (${\mathrm{B}}_{2g}$) order, we find a preemptive transition into low- and high-temperature vestigial phases with loop-current and nematic order corresponding to $xy$ (${\mathrm{B}}_{2g}$) and ${x}^{2}\ensuremath{-}{y}^{2}$ (${\mathrm{B}}_{1g}$) symmetry, respectively. Near the transition between the two phases, a state of soft nematic order emerges for which we expect that the nematic director is readily pinned away from the high-symmetry directions in the presence of an external field. Results are discussed in relation to findings in the cuprates, especially to the recently inferred highly anisotropic superconducting fluctuations [W\aa{}rdh et al., arXiv:2203.06769], giving additional evidence for an underlying ubiquitous PDW instability in these materials.