I don't know about friendlies, but I've seen a few lopsided matches on the net here. But both were official matches though... I would imagine it to be rarer in friendlies with nothing on the line and more emphasis on fitness and preserving players from injury than throttling your opponents... One was this South African NedBank Cup match in which Mamelodi Sundowns beat 3rd tier Powerlines FC 24-nil... Then there was this World Cup qualifier which was a highlight of why Australia escaping Oceania was a blessing for both parties, 31-nil...
The biggest I know of is Micronesia losing 46-0 to Vanuatu. The sad thing is that back in 2001 this FIFA article mentioned that Micronesia applied for membership. It also mentioned New Caledonia. New Caledonia became a member and Micronesia did not and look at the difference since then. Not sure what went wrong but who knows how much better they'd be if they had made it. Many people don't realize that FIFA members get $250K per year (new FIFA president said it will go up) with GOAL projects worth up to $500K every few years as needed. That's a lot of money for smaller countries to be able to improve soccer development as long as the money is used in the right way.
I don't know how New Caledonia and Micronesia are doing financially, but New Caledonia is 183rd in the FIFA Rankings, so it's not like they're a good national team. There is a big difference in the ELO Ratings with New Caledonia in 118th and Micronesia in 222nd, but regardless of what ranking you go by you wouldn't expect New Caledonia to qualify for a World Cup anytime soon.
I am currently reading Kicker 1971 and noticed that in 1970-71 a lower league club called TSV Sattelpeilnstein recorded a season of 100 % defeats with scoring 9 goals and conceding 236 goals. On average they thus condeded 10 goals per game. These were competitive games, not friendlies (League: C-Class East IV of Amberg-Schwandorf-Cham).
There's a similar record going on with Longford AFC last season in the Gloucestershire Northern Senior League Division Two (level 13 in the FA pyramid). After 16 games they had scored zero and conceded 170, before finally managing to score on January 13th. They managed to coax Stuart Pearce into playing a couple of games for them and did improve towards the end of the year, finishing with "only" 226 goals conceded in 30 games (so 56 in the last 14). http://full-time.thefa.com/Table.do?divisionseason=880971293
The funding that members receive from FIFA isn't so much about turning countries into World Cup contenders and more about growing and developing the game in those countries and helping them achieve their full potential. For example, New Caledonia will always have an advantage over Micronesia because they have twice the population and being a former French colony, they are much more involved with soccer. Just like Martinique and Guadeloupe will always be better than many Caribbean countries and territories that are FIFA members. Since becoming FIFA members, New Caledonia has received four GOAL projects on top of the yearly FIFA payments to all members. During last month's Oceania Nation's Cup they lost 1-0 to New Zealand in the semifinals. Hard to see that happening without any assistance. Micronesia probably could never aspire to get the same results, but if they had the same assistance as New Caledonia had during the same time, it probably would've been realistic to see them lose only by single digits at the Pacific Games.