I am not sure what your goal is. Do you want a vector with 13 elements where everything is treated as a number? Would the 13th element be the calculated result of 22334455/55443322? Or do you want a numeric vector with 26 elements where the character / has been treated as a delimiter? I would do that like this:
library(stringr)
library(purrr)
OUT <- str_split(c("11111111",
"22222222/ 33333333/ 44444444",
"55555555/ 66666666",
"77777777",
"88888888",
"99999999/ 987654321/ 12345678/ 22334455",
"44556677/ 88990011/ 11223344/55667788",
"23456789 /98765432",
"34567890/ 09876543",
"09873467",
"33445667",
"88997766/ 12345678",
"22334455/ 55443322"),"/")
OUT_numeric <- map(OUT,.f = as.numeric)
OUT_numeric
[[1]]
[1] 11111111
[[2]]
[1] 22222222 33333333 44444444
[[3]]
[1] 55555555 66666666
[[4]]
[1] 77777777
[[5]]
[1] 88888888
[[6]]
[1] 99999999 987654321 12345678 22334455
[[7]]
[1] 44556677 88990011 11223344 55667788
[[8]]
[1] 23456789 98765432
[[9]]
[1] 34567890 9876543
[[10]]
[1] 9873467
[[11]]
[1] 33445667
[[12]]
[1] 88997766 12345678
[[13]]
[1] 22334455 55443322
FINAL <- unlist(OUT_numeric)
class(FINAL)
[1] "numeric"
FINAL
[1] 11111111 22222222 33333333 44444444 55555555 66666666
[7] 77777777 88888888 99999999 987654321 12345678 22334455
[13] 44556677 88990011 11223344 55667788 23456789 98765432
[19] 34567890 9876543 9873467 33445667 88997766 12345678
[25] 22334455 55443322