Welsh, Gaelic, and Scots Gaelic are interesting examples, but the last two in particular, don't fit in all the way. The language never lost native speakers entirely, only most of them. In parts of West Ireland Gaelic remained stronger than English throughout, while in Scotland the same can be said for Sctos Gaelic in the Highlands. I think with Welsh you have a slightly better case, but not quite enough.
Another language I was thinking of that lost, if I remember correctly, all of its native speakers was Cornish. In that case the Corns are not even recognized by the British government as beign seperate in culture from the in English in any way more than the position of Duke of Cornwall. This lack of respect from the ruling nation and the relative poverty of the Corns in relation to English and other British Celts resulted in them giving up their language and much of their culture, yet they still maintianed a good level of uniqueness to them.
Another example would be Breton, a Celtic language now spoken by only a few people in Brittany, France. The French government has not alloud language preservation movements in their country, this has stiffled any chance for Breton revitalization. Yet, the Bretons remain extremely unique. They tend to appear to be a mix of the more traditionally associated Celtic peoplese (Ireland, Scotland, Wales, etc.) and the neighboring French.
Furthermore, you can see an example of people giving up their language when Italian and French were derived and made into the official languages of much larger areas than in which they were originally spoken. When French was introduced, the other oil languages nearly disapeared completely. In fact, those that have survived (an ever smaller number) have been mitigated to the poition of French dialects, rather than individual languages. The same can be said of Italy. In Italy each of the regions, and sometimes subregions, had its own language. Today the only relativley secure pre-Italian Italian language is Sicilian (although some of the northern languages have been given a boost in recent years). Griko is spoken by only a scattering of Calabrese and Puglise, while both of the regional languages have disapeared. Sradinian is likely to go in one or two generations, and the same can be said of most of the south and central Italian languages. The people of both Italy and france willingly gave up their languages in order to attain both the national unity and acceptance that would come with adopting the new French and Italian languages.
Furthermore, another very good example would be the Normans. They were a Viking culture that undoubtably spoke a Norse dialect, but when they settled in France they adopted the French language within only a couple generations, wuite willingly I might add. Whiel they adopted many French cultural traits, they maintianed many of their own individual ones. For instance, they maintained a very militaristic and seafaring culture that allowed them to later on conquer England, Ireland, Siciliy, Southern Italy, and numerous other conquest here and there. Then, when they moved on to England and other areas, they quickly adopted the language of that civilization. It took a few generations, but the English Normans adopted English, as did the Scilian Normans Sicilian, the Calibrese Normans Calibrese, etc.
I am quite sure that there are numerous other examplesto draw on. For instance, many Native American languages. However, it seems to me that the above examples should be more than enough to prove the fact that it is possible for a people to give up their native tongue in favor of another language.