Linux – Executable Fails with ‘File Not Found’ Even in PATH

I want to launch the wine executable (Version 2.12), but I get the following error ($=shell prompt):

$ wine
bash: /usr/bin/wine: No such file or directory
$ /usr/bin/wine
bash: /usr/bin/wine: No such file or directory
$ cd /usr/bin
$ ./wine
bash: ./wine: No such file or directory

However, the file is there:

$ which wine
/usr/bin/wine

The executable definitely is there and no dead symlink:

$ stat /usr/bin/wine
  File: /usr/bin/wine
  Size: 9712            Blocks: 24         IO Block: 4096   regular file
Device: 802h/2050d      Inode: 415789      Links: 1
Access: (0755/-rwxr-xr-x)  Uid: (    0/    root)   Gid: (    0/    root)
Access: 2017-07-13 13:53:00.000000000 +0200
Modify: 2017-07-08 03:42:45.000000000 +0200
Change: 2017-07-13 13:53:00.817346043 +0200
 Birth: -

It is a 32-bit ELF:

$ file /usr/bin/wine
/usr/bin/wine: ELF 32-bit LSB executable, Intel 80386, version 1 (SYSV), 
dynamically linked, interpreter /lib/ld-linux.so.2, for GNU/Linux 2.6.32, 
BuildID[sha1]=eaf6de433d8196e746c95d352e0258fe2b65ae24, stripped

I can get the dynamic section of the executable:

$ readelf -d /usr/bin/wine
Dynamic section at offset 0x1efc contains 27 entries:
  Tag        Type                         Name/Value
 0x00000001 (NEEDED)                     Shared library: [libwine.so.1]
 0x00000001 (NEEDED)                     Shared library: [libpthread.so.0]
 0x00000001 (NEEDED)                     Shared library: [libc.so.6]
 0x0000001d (RUNPATH)                    Library runpath: [$ORIGIN/../lib32]
 0x0000000c (INIT)                       0x7c000854
 0x0000000d (FINI)                       0x7c000e54
 [more addresses without file names]

However, I cannot list the shared object dependencies using ldd:

$ ldd /usr/bin/wine
/usr/bin/ldd: line 117: /usr/bin/wine: No such file or directory

strace shows:

execve("/usr/bin/wine", ["wine"], 0x7fff20dc8730 /* 66 vars */) = -1 ENOENT (No such file or directory)
fstat(2, {st_mode=S_IFCHR|0620, st_rdev=makedev(136, 4), ...}) = 0
write(2, "strace: exec: No such file or di"..., 40strace: exec: No such file or directory
) = 40
getpid()                                = 23783
exit_group(1)                           = ?
+++ exited with 1 +++

Edited to add suggestion by @jww: The problem appears to happen before dynamically linked libraries are requested, because no ld debug messages are generated:

$ LD_DEBUG=all wine
bash: /usr/bin/wine: No such file or directory

Even when only printing the possible values of LD_DEBUG, the error occurs instead

$ LD_DEBUG=help wine
bash: /usr/bin/wine: No such file or directory

Edited to add suggestion of @Raman Sailopal: The problem seems to lie within the executable, as copying the contents of /usr/bin/wine to another already created file produces the same error

root:bin # cp cat testcmd    

root:bin # testcmd --help
Usage: testcmd [OPTION]... [FILE]...
Concatenate FILE(s) to standard output.
[rest of cat help page]

root:bin # dd if=wine of=testcmd  
18+1 records in
18+1 records out
9712 bytes (9.7 kB, 9.5 KiB) copied, 0.000404061 s, 24.0 MB/s

root:bin # testcmd
bash: /usr/bin/testcmd: No such file or directory

What is the problem or what can I do to find out which file or directory is missing?

uname -a:

Linux laptop 4.11.3-1-ARCH #1 SMP PREEMPT Sun May 28 10:40:17 CEST 2017 x86_64 GNU/Linux