What is the current accepted theory for the fate of hot Jupiters?
This is a fairly loaded question in that it depends heavily on what a "hot Jupiter" actually is defined to be. What is "hot"? What is a "Jupiter"? In reality, there's a continuum of planetary masses and distances from their parent star, and in the literature you'll commonly see references to "hot Neptunes", "hot Saturns," etc.

The predominant theory as to how giant planets form is that they first coalesce from rock and ice beyond the ice line, the distance from the parent star at which water becomes solid. This distance is approximately where Mars lies today in our solar system. What's surprising about "hot gas planets" is that they are found within this ice line, significantly within. This implies that after they formed their cores, they migrated closer to their host stars via some currently undetermined process (for which there are several good candidates, but for now let's assume that the existence of hot planets shows that at least one of these processes operates quite regularly).

And what about the word "hot"? Well, for the planets that are closest to their parent stars, there is known to be a radius anomaly: The radii of these planets are significantly larger than models of giant planet structure irradiated by their host stars would predict. So I would define "hot" planets as gas giants whose radii are larger than what would be predicted by the standard models.

Now that we got some of the definitions out of the way, there's the question of survival. When giant planets are close to their parent stars, they become tidally locked. As a consequence, there is very little energy tidally dissipated on the surface of the giant planet, the shape of the planet is fixed and there are little internal motions. However, the giant planet also raises a tide on its host star as well, and because it takes a lot of angular momentum to change the spin of an object with 1,000 times more mass, the host stars are almost never going to be tidally locked to their closest planet.

The rate at which energy is dissipated within the star is highly uncertain, and this uncertainty is typically swept into a fudge parameter "Q," the quality factor, with lower quality factors reflecting more dissipation. "Q" is measured for certain bodies in our own solar system (i.e. Earth and Jupiter) and in some stellar binaries, but is highly variable from body to body, ranging from about 10 for the Earth to 10^8 for some stars.

Whether a planet survives to be observed today depends on how long the orbital decay time, which is determined by Q, compares to the age of the system. For some systems, such as WASP-12b and WASP-19b, which feature highly inflated hot Jupiters, Q is estimated to be small enough to cause them to fall into their host stars in a surprisingly short time (&lt; 10^7 years).

One other possibility is that the gas surrounding the rock/ice core is blasted away by the tremendous amount of heat deposited into the planet. This leaves you with a relatively low-density planet that's somewhat devoid of iron, as the cores of giant planets form further from their host stars than the rocky planets. There are a few candidate close-in, Neptune-mass objects that may have been produced as a result of them losing the bulk of their atmospheres in this way (Example: GJ3470b).

As for our own solar system, the formation of a hot Jupiter would have likely destroyed the inner solar system as it migrated close to the Sun, owing to the fact that it would violently perturb the inner planets' orbits. Additionally, the Sun would likely be enhanced in metals owing to the accretion of metal-rich material from this giant planet. While it's potentially possible that there was a hot Jupiter in our solar system before the other planets formed, it currently seems unlikely.