I'll say right off the bat that it would be damn hard to prove. 2700 years of genetic mixing and migration, and total uncertainty about the "ethnic" make up of Iron Age Israel would have been would make it hard to prove anything. You could do genetic testing on remains found in the region, but how you'd actually prove they were Israelite bones is beyond me.

And that brings me to the other issue. The "10 Lost Tribes" are a legend. Maybe there's truth to it, but that doesn't make them any less legendary. We don't know nearly as much about the Iron Age Hebrew kingdoms as we'd like, or how much historical truth there is in the 12 Biblical tribes. There seems to have been truth enough in the Levites, but anything else is sketchy at best. Fortunately, the most important detail about the Lost Tribes, ie the circumstances of losing them, is actually a verifiable historic event.

So, laying out the bare facts: in the late 8th century BCE there were two Hebrew kingdoms. According to the Bible they shared a common religion and culture, but had seperate governments. To the south was Judah and to the north was Israel. Even at that time, Israel was often called "Samaria," the name of its capital city, in many sources. Eventually, Israel/Samaria became associated with 10 of the 12 Hebrew tribes in the Torah. Whether it was at this point, we don't know. The major power in the region at this point was Assyria, and they seem to have been content with making the Israelites/Samaritans into tribute paying vassals, but the Israelites weren't having it. They participated in several rebellions against Assyria and in 722, Samaria was sacked and its people deported, along with a large chunk of the surrounding population. 27,000 people according to Assyrian inscription.

Where exactly they were deported to is somewhat unclear, but it seems that it was recently subdued region in the northeast of the empire, so somewhere between around the north of modern Iraq. However, that 27,000 figure is interesting. Because it's big enough to reflect the whole population, if it was sparse, but small enough to leave room for a significant population to remain. Not to mention, its always safer to assume the Assyrians were exaggerating. A smaller population of deportees from elsewhere were brought in to keep working the land and paying taxes for the new province of the Assyrian Empire.

Now, we also need to know who the hell the 10 Lost Tribes were to the people who originally developed that story. Were they the whole population of Israel/Samaria? That's what the Bible kind of implies, but is also the least likely based on the other facts, including and especially the Biblical evidence. The numbers seem to indicate that some of the original Samaritans stuck around, so how could they be considered lost? That leaves a few other options.

First, maybe the 10 Lost Tribes are strictly the deportees and were original interpreted as lost members of the 10 tribes. That would throw a bit of a wrench in the Palestinian connection, but also doesn't really add up. The story of the 10 tribes as it has developed and persisted in the present is pretty firm that all 10 tribes vanished wholesale.

Next up, there's the pretty likely possibility that the Hebrews were more of a ruling class who took over the area and ruled over the native Canaanite population. This seems likely from the historic evidence and the elites and skilled workers would have been the first victims of deportation.

The final option is that the 10 Tribes were only the Yahweh worshippers. This is still the period where most scholars think Judaism was developing monotheism out of Canaanite pagan religion. Personally, I favor a combination of these last two theories.

Regardless of whether the 10 Tribes existed as 10 literal tribes, the ruling class and any strict monotheists in Samaria vanished in the deportation. The Samaritans tendency to bend the rules of Judaism and mix with local pagan traditions became a staple complaint of the Judahites, and later Judeans through the 1st century CE. That's the offense that the Old Testament prophets say caused God to allow the Assyrian conquest and in the New Testament a "good Samaritan" is apparently still something that shocked a Jewish audience.

Any Yahweh monotheists in Samaria were apparently deported, assimilated, or moved to Judah, and like I said, the ruling elite - who may have included all the monotheists anyway, were moved to Mesopotamia. But don't lose hope on your theory. A few decades later, the Judahite elite were also exiled by the Babylonians, and a few decades after that, the Persians gave their territory back and ended the practice of deportation. If there were any surviving "Jews" from the Assyrian deportation then maybe they also traveled back to Judah.

However, there was also a flourishing Jewish diaspora by the Hellenistic period that they may have been incorporated into, and it's just as likely that they simply assimilated into their new homes.

So, are the Palestinians descended from the 10 Lost Tribes? Maybe, depending on how you define them. In they are, modern Jews are probably also descended from them. There's no doubt some populations Syria/Iraq/Iran are connected too, and that whole region has come under so many empires that their descendants could be spread from Morocco to Siberia by now.

It's been over 2000 years, closer to 3000. That's plenty of time to get descendants anywhere you want them to be. I think the important question about the 10 Lost Tribes isn't "Where did they go?" but "What did that mean to the people who lost them?"