Kjustendil is a small city in Bulgaria. Around 45,000 people live here.
Kyustendil has a sort of ring road. If your driver is going into Kyustendil and you're not, it is an option to take this ring road. Since the border crossing to North Macedonia is very small and the only reason to go further west after Kyustendil, traffic is very scarce and people are reluctant to stop for you as this road passes through a Roma neighborhood and Bulgarians here are not very fond of the Roma. You probably will succeed in passing Kyustendil this way, but it will take you a long time. It might be a better idea to ask your driver to drop you off at the western part of the city or walk half an hour west from the city center to where the local road meets the highway again.