Self-jumpstarting means jumpstarting one's own vehicle without the use of another vehicle. The most common way to do this is by combining house and chassis batteries.
It will be gentlest on the system to combine the batteries and allow the starter battery to come up a bit instead of immediately attempting to start.
This will be easiest if one already has some kind of isolator/combiner setup. If not, one can run jumper cables from the house bank, or physically remove the house bank and carry it to the starter battery area.
Switches used as manual isolators will self-jumpstart when in the ON position.
Solenoids/relays always self-jumpstart assuming there is enough voltage in the starter battery to energize the solenoid.1) It is a mechanical connection and power will flow both ways.
Some VSRs have a provision to combine the batteries for self-jumpstarting.
As with diode-based isolators, DC-DC chargers on their own cannot pass power back from the battery bank to the vehicle. Read below for workarounds and different approaches.
It adds a layer of complexity, but a relay with a switch can be used to bridge the batteries manually.
Note the Smartpass does this when added to the CTEK D250-series chargers.
Some combo DC-DC chargers contain logic to maintain the starter battery when solar power is present.
Some standalone solar charge controllers like the Morningstar SunSaver Duo can, for example, charge the start battery with 10% of solar harvest and the house battery with 90% using different charging profiles. As with DC-DC above, it's not self-jumpstarting but can help prevent the dead starter battery.
Lithium "jump packs" have become more popular. Lithium-chemistry batteries can discharge quickly, so even relative small packs can jumpstart a car.
'Dwellers may want to pick a jump pack that has 12v or USB outlets so it can have other uses.