partial matching of strings in different two datasets to obtain a match with higher frequency

This dplyr method doesn't need a join (which is reasonable as you don't have a common column to join on). It combines the 2 datasets and finds the matches. As long as you don't have thousands of rows it will work fast enough. Of course you can make the script smaller, but you can run this step by step to see how it works.

df1<- data.frame(A=c(.87,.11,.44,.45), B=c("I have a beard", "I slept for two hours", "I have had two courses","this is not true"))

df2<- data.frame(X=c(127,10,433,344,890,4),Y=c("have","beard","syllabus","true","three","maths"))

library(dplyr)

df1 %>% 
  rowwise() %>%
  do(data.frame(.,df2)) %>%                    # combine datasets
  do(data.frame(.,flag = grepl(.$Y,.$B))) %>%  # for each row check if there's a match and name it flag
  ungroup %>%
  group_by(A,B) %>%                            # for each A and B
  mutate(N=sum(flag)) %>%                      # count how many matches you have
  filter(flag==TRUE | N == 0) %>%              # keep only A,B where you have some matches or no match at all
  top_n(1,X) %>%                               # pick one row based on max value of X
  ungroup %>%
  mutate(Y = ifelse(flag==FALSE,NA,as.character(Y)),   # if there's no match replace Y with NA
         X = ifelse(flag==FALSE,NA,X)) %>%             # if there's no match replace X with NA
  select(-c(flag,N)) 


#      A                      B   X    Y
# 1 0.87         I have a beard 127 have
# 2 0.11  I slept for two hours  NA   NA
# 3 0.44 I have had two courses 127 have
# 4 0.45       this is not true 344 true

Try to experiment and change various column values to see how it works. You might be able to spot any bugs in advance.