Can I run a sub without an amp?

You cant run a sub strictly off of RCAs. You can run one off of one of the channels of an HU (Or bridge the rear two channels, if thats even possible with an HU) Otherwise you need an amp. You shouldnt run subs off the HU alone cause the powers too low. Its only 20W rms the most.

How do you connect a subwoofer to a passive speaker?

The first, most effortless way of joining the powered subwoofers with passive speakers is using a stereo RCA. Sometimes speakers dont have the LFE connections. In that case, you have to use the RCA connection. RCA connection is the point of connecting any audio video device with your speakers.