When the lava comes up and flows across the surface I assume a large void is left where it came from. Does this large void have any impact on anything down the line once the flow stops?
I would tend to assume that no large voids will be formed. Magma would be pushed out by the weight of the material above it. As the magma flows up and out, the crust above it will sink and not allow the formation of large voids. If for some reason, the crust can’t sink then pressure must abate and the magma will stop flowing.
Smaller voids and lava tubs will form as a result of the ebb and flow of magma but other than providing a potential path to the surface for a future eruption, nothing too dramatic is likely to happen.
I’m sure smarter people than I will be along shortly to explain my level of schmuckery.
Large is a relative term.
It might seem to us that a lot of lava has been deposited in the recent flows in Hawaii but compared to the volume of the mantle it’s insignificant.
The magma in the magma chambers is under considerable pressure, so after an eruption this pressure is reduced at that locality.
Volcanic cones also tend to collapse as the lava flows out from other locations. This material may not fill the void underneath it which can then fill with steam if the void is below the water table, and that results in huge sudden eruptions if the steam can’t vent fast enough.
If lava flows out too quickly and is not replaced fast enough, the magma chamber can collapse and form a caldera, which is basically a sinkhole.
A classic example is Crater Lake in Oregon. However, much of the Yellowstone area consists of enormous calderas.
There are lava tubes, cave-like voids left over after underground flows have cooled. I recently visited Lava River Cave in Oregon–a mile long lava tube that you can check out on your own. Pretty amazing place.
edit: I think Alpha Twit mentioned them in his post, but left the “e” off.
My favorite example of massive volcanic floods are the Columbia River Basalt Floods.
In some places they add up to more than a mile high. But the ground underneath sank. And since a lot of the basalt flowed out from the area of the source(s), some places actually ended up lower than before. That’s a lot of sinking!
Think of it like applying pressure to pop a zit. The gunk comes out and the skin pushes in to fill the area where the goo was. Sometimes you’re left with smoothish skin, sometimes you get a crater. But you shouldn’t get an air space.
If there were a void left behind, why would the lava have erupted to the surface? Rock is actually quite heavy.[sup][citation needed][/sup] It doesn’t just levitate out of its subsurface chamber, it has to be pushed out, by the considerable pressure of the rock above and all around it.
Aren’t calderas also formed by massive explosive eruptions? I was under the impression that, for example, the Long Valley Caldera in California was the result of blowout eruptions, more than collapsed lava domes.
An eruption can produce both effects: Blowing off the top of the volcano, and subsequent collapse of the magma chamber and formation of a caldera.
The Wiki page on Long Valley Caldera indicates it was partially produced by the collapse of a magma chamber, plus pyroclastic eruptions.
I am not a geologist, but as far as I know a caldera is formed by subsidence by definition. A hole produced by an explosion is a crater. Of course, some volcanoes combine both kinds of features.
Caldera: a sinking of the ground due to expulsion of the magma underneath.
Crater: A buildup of ejecta around a volcanic vent.
Not according to Merriam-Webster.
Now, of course, Merriam-Webster isn’t a geological authority. So perhaps someone who is a geologist can come along and cite a more comprehensive authority that indicates that a caldera requires a collapsed structure. Finding a more comprehensive authority certainly shouldn’t be difficult; I’m not going to go banco on Merriam-Webster. 
This is what’s happening at Kilauea, according to theUSGS update site:
A concern is that if it subsides in a particular way, an opening or void can be created which fills with ground water, then sealed too close to the magma; the water then boils and boom.