Using transport="stdio" closes real stdio, causing ValueError after server exits

Initial Checks

• I confirm that I'm using the latest version of MCP Python SDK
• I confirm that I searched for my issue in https://github.com/modelcontextprotocol/python-sdk/issues before opening this issue

Description

Hi! I ran into an issue where running the server with transport="stdio" causes subsequent stdio operations to fail after the server exits.

Minimal reproduction

from mcp.server.fastmcp import FastMCP

mcp = FastMCP("Demo")
mcp.run(transport="stdio")
print("?")

When using Ctrl+D to exit the server, the final print raises:

Traceback (most recent call last):
  File "...", line 5, in <module>
    print("?")
ValueError: I/O operation on closed file.

I’m not sure if this is intended behavior though.

Likely cause

In stdio.py, stdio is wrapped like this:
https://github.com/modelcontextprotocol/python-sdk/blob/5301298225968ce0fa8ae62870f950709da14dc6/src/mcp/server/stdio.py#L44-L47

When these wrappers are closed, they also close the sys.stdin.buffer / sys.stdout.buffer.

Proposed fix

    if not stdin:
        stdin_fd = os.dup(sys.stdin.fileno())
        stdin_bin = os.fdopen(stdin_fd, "rb", closefd=True)
        stdin = anyio.wrap_file(TextIOWrapper(stdin_bin, encoding="utf-8"))
    if not stdout:
        stdout_fd = os.dup(sys.stdout.fileno())
        stdout_bin = os.fdopen(stdout_fd, "wb", closefd=True)
        stdout = anyio.wrap_file(TextIOWrapper(stdout_bin, encoding="utf-8"))

Python & MCP Python SDK

Python 3.10.15
mcp==1.25.0

Inizia in src/mcp/server/stdio.py, nella configurazione del wrapper intorno alle righe collegate, quindi esegui la riproduzione minima di FastMCP riportata nell'issue. Conferma che la chiusura dei wrapper stdio non chiuda più gli stream standard reali del processo e verifica che il print finale abbia esito positivo dopo l'uscita del server.