In 1963 the US 13 designation was extended about 50 miles southwest from its former terminus in Goldsboro to Eastover NC. So at that time US 13 attained its maximum length and its current route, which is shown as a thin blue line on this map:
The proposal was resubmitted at least twice (in 1968 and 1969), but it was rejected each time by AASHO's US Route Numbering Committee. It would have been unusual to have US 13 ending at its junction with a state highway (SC 28), and Abbeville's proximity to the state line suggests that the ultimate plan may have been to extend US 13 to Athens GA. However, an extension into Georgia was not included in the proposals to AASHO, and that may have been one of the reasons it was not approved. More about US 13's current and historic endpoints can be found on the US 13 page.
*AASHO became AASHTO in 1973.