I can only speak as a Maltese here, but we kinda didn't. For most of its existence Malta was under dominion by sometimes else (which can be seen within its culture and Semitic language influenced immensely by Italian and French) almost continuously from the Phoenicians to the British. The most influential of those, whose influence can still be seen today, would be the Fatimids (220 years), the Knights of St. John (275 years) and the British (some 165 years).

The Knights of St. John were something of an independent entity from the rest of Europe who were given the island by Emperor Charles V in an attempt to stop Ottoman expansion in the Mediterranean, and while they depended heavily on European Catholic backing, and were all from a European background (none local), they were also their own polity.

Independence only came peacefully in 1964 from the British, which Malta later followed by adopting a Yugoslavian-like stance of neutrality between the First World, the Second World and the Third World (with a close alliance to Gaddafhi's Libya during Mintoff's tenure).

It's also important to note that independence was not always seen as the only option. There have been historical local political desires to either be absorbed into Italy (something which was also of interest to Mussolini) or the United Kingdom.

You can also find some oddities, like the Independence of Gozo for two years from Napoleonic France in the Second Siege of Malta, in which the other inhabited island in what is today the Republic of Malta (there's also Comino, but almost nobody lives there other then a family, some people working in a hotel and a lot of lizards) gained independence from the French for two years after booting the French out, before the British united it back into the Malta Protectorate.

Malta was a possession of larger powers for millennia (and not ever really an "independent state", so I don't know that you could say it was absorbed) before achieving independence from the U.K. in 1964. At various points it was Phoenician, Roman, Moorish, Norman, a part of Aragon, a part of the larger Spanish Empire, occupied by the Knights of St. John of Jerusalem (the "Knights of Malta", though previously of Rhodes), France, and Great Britain. It is quite possible I've left someone out there too. Malta is uniquely placed in the Mediterranean Sea, at a sort of strategically important "crossroads" of ship traffic. As such, it has been historically important to great powers for a very long time.

Liechtenstein came into existence as one of many hundreds of smaller states making up the Holy Roman Empire. The princes of Liechtenstein were closely tied to the ruling Hapsburg family of the HRE, who later rule the Austro-Hungarian Empire. When the AHE collapsed after the First World War the princes of Liechtenstein resisted merger into the newly created state of Austria in favor of continued independence. This was partially supported historically, as the Hapsburg emperors had declared Liechtenstein an independent principality within the HRE some centuries before, and Liechtenstein was never formally annexed into the AHE. So, it was in something of a limbo. Liechtenstein maintained independence through World War Two by maintaining neutrality. The Nazis never invaded, and it was left largely alone. After WW2 Liechtenstein's major selling point has been its very low tax rate... it has become a tax haven, like various other small countries. And very successfully too.

Microstates that have a longer history tend to have survived because they 1) posed no threat to larger powers, and 2) offered something of benefit to larger powers (neutral ground, banking, etc.).

Check out: Neumann, I.B. & Gstöhl, S., 2004. Lilliputians in Gulliver’s World ? Small States in International Relations.

also, Raton, Pierre (1970). Liechtenstein: History and Institutions of the Principality.

Also, the Wikipedia article on the history of Malta is pretty thorough.

For those two countries, the answer is that they didn't. Neither became fully independent until the twentieth century.

Liechtenstein is a rather funny case. It was originally the personal property of an aristocratic Austrian family. They bought it in order to qualify for a seat on the Imperial diet of the Holy Roman Empire. It was elevated to be a principality by the emperor and became a member state of the HRE. During the period when Liechtenstein was part of the HRE (and later the Austrian and Austro-Hungarian empires), the royal family didn't even live there for most of the time. When the Austro-Hungarian empire was broken up after the end of WWI, Liechtenstein became an independent country.