You have to have a hydrostatic column of fluid that exerts a higher pressure on the reservoir formation than the pore pressure in the reservoir. So, for example, in the depleted reservoir I'm working on, with a pressure of approx. 3500psi at 8300ft TVD, the mud weight needed to be greater than the pore pressure is about 8.1ppg:- 3500/ 8300 = 0.4217psi/ft; 0.4217 /0.052 = 8.1ppg. So seawater, at 8.7ppg will kill the well, if you can stop it flowing away into the reservoir. In order to do this we use a perflo pill, (which is a trade name for sized CaCO3), to block the pores in the reservoir formation, similar to how a mud filter cake works, which can be easily removed when we want to bring the well back on.
You wouldn't used mud to kill a well you want to bring back on, as you will proabaly have problems getting the well to flow again- you'd use the various solids-free brines that are available at variuos weights up to 16ppg: NaCl, bromides, formates, whatever, with a pill to stop the brines flowing away into the reservoir.
If you're killing the well before plugging & abandoning it, you'd use mud, probably the mud you've been using to drill the well.