Why did the Liberal Democrats collapse?

[Cassius]

By entering government with the Tories, they in one stroke alienated two of their biggest voting blocs - dissatisfied centre-leftists who voted for them to protest against Iraq/New Labour/Corruption, and generic protest voters who didn't particularly like either of the two main parties and viewed the Lib Dems as a suitable means to express this dislike. Furthermore, once they were in government they compounded this alienation by, as Vosem said, doing a complete volte face on several key parts of their platform, most notably of course tuition fees, and more generally in acquiescing to many of Osborne's other 'austerity' measures. They then drove themselves further into the ground by cocking up the campaign for electoral reform (which was the only thing they really had to gain from participating in the coalition) and by being generally incompetent. The party was also dogged by scandals throughout its time in government (David Laws, Chris Huhne and Lord Rennard to name but a few), which perhaps had the effect of further reminding voters that the Lib Dems weren't really that different from the 'old parties' at all, at least when it came to scandals. Also Nick Clegg was the face of the party throughout this time, and he was about as popular as cancer (whilst, obviously, this came about largely as a result of his decision to take the Lib Dem into coalition and break several of their key election pledges, I do think there is also something to be said for the fact that his grating and sanctimonious personality wasn't exactly a help in this regard).

The Lib Dems have always had various (often overlapping) blocs of support - lifelong Liberals who had supported the old Liberal party, ex-SDPers, the aforementioned generic protest voters, anti-Blair centre-leftists, anti-Tory tactical voters, people who voted Lib Dem chiefly on the basis of the local candidate, gene pool supporters from the West Country and rural Wales and Scotland and, last but perhaps not least, people who were, perhaps, moderately centre-right and conservative who nonetheless didn't support the Tories due to the party's very negative image in the 1990's and 2000's. Going into government, with the Tories, utterly alienated several of these blocs, and the Tories were able to eat into the last group by proving themselves not completely heartless and incompetent in the 2010-15 government (at least, from the perspective of the voters in said bloc). The Lib Dems were basically reduced to a rump of their most traditional supporters, voters who strongly supported the local MP and perhaps a few of the centre-right types, and taken together this ultimately didn't amount to very much.