What have I got in my pocket?
Python 2.7 571 542 509

import sys
o,l,v,k,w="MYPOCKET",[list(e)for e in sys.stdin],[],enumerate,len
def f(z,q,t):
 for r,c in(z,q+1),(z,q-1),(z+1,q),(z-1,q):
  if w(l)&gt;r&gt;=0 and 0&lt;=c&lt;w(l[r])and o[t]==l[r][c]:
    v.append((r,c))
    if f(r,c,(t+1)%w(o)):return 1
    else:v.pop()
 if z==1 and(0,q)in v or z==0 and(z,q+1)in v:return 1
for i,x in k(l[0]):
 v=[(0,i)]
 if x==o[0]and f(0,i,1):break
for i in range(1,w(l)-1):b=[y for x,y in sorted(v)if x==i];print"".join(["".join(e)if w(e)&gt;0 else" "for e in[l[i][b[j-1]+1:y]for j,y in k(b)][1:]])


Works as a program(banking on a recursive function) and accepting input from stdin.
Demo here.Testing it (ex1.txt and ex2.txt are the examples from the question)- 

$ python pockets.py &lt; ex1.txt
F
BND
EUF
SNDUW
BOVUV
ENWF
$ python pockets.py &lt; ex2.txt 
  HA 
NDSES
 HA  


Ungolfed version with comments - 


s="""
EKCYMOPD
KCOPHAYM
EKNDSEST
JETHACKE
KRMYPOBN
"""
li2=[list(e.strip()) for e in s.split("\n") if e.strip()!='']
buf=[]
def find_precious(row, col, c_ind):
    for r,c in[(row,col+1),(row,col-1),(row+1,col),(row-1,col)]:
        if len(li2)&gt;r&gt;=0 and 0&lt;=c&lt;len(li2[r]) and seq[c_ind]==li2[r][c]:
            if (r,c)in buf:return True
            buf.append((r,c))
            if find_precious(r,c,(c_ind+1)%len(seq)):return True
            else:buf.pop()
    if row==1 and (row-1,col) in buf or row==0 and (row,col+1) in buf:return True
    return False

for i,x in enumerate(li2[0]):
    if x==seq[0]:
        buf=[(0,i)]
        if find_precious(0,i,1):break
if len(buf)==1:
    exit("Failed")

#Calculate the middle men
for i in range(1,len(li2)-1):
    b=[y for x,y in sorted(buf)if x==i]
    print "".join(["".join(e)for e in [li2[i][b[j-1]+1:y]for j,y in enumerate(b)][1:]if len(e)&gt;0])


Let me know, if I did something stupid or something can be done better.
I know it's looong, but it's the best I could do :P