Deep defects in silicon carbide (SiC) possess atom-like electronic, spin and optical properties, making them ideal for quantum-computing and -sensing applications. In these applications, deep defects are often placed within fabricated nanostructures that modify defect properties due to surface and quantum confinement effects. Thus far, theoretical studies exploring deep defects in SiC have ignored these effects. Using density functional theory, this work demonstrates site-dependence of properties of bright, negatively-charged silicon monovacancies within a SiC nanowire. It is shown that the optical properties of defects depend strongly on the hybridization of the defect states with the surface states and on the structural changes allowed by proximity to the surfaces. Additionally, the analysis of the first principles results indicates that the charge-state conversion and/or migration to thermodynamically-favorable undercoordinated surface sites can deteriorate deep-defect properties. These results illustrate the importance of considering how finite-size effects tune defect properties, and of creating mitigating protocols to ensure a defect's charge-state stability within nanostructured hosts.