If I unlock an encrypted wallet for 359711509437336256 or less seconds, I can sign transactions with it:

    $ bitcoin-cli walletpassphrase "$x" 359711509437336256
    $ echo $?
    0
    $ bitcoin-cli signrawtransaction $tx | grep complete
      "complete": true

But if I unlock it for 359711509437336257 or more seconds, it appears to have unlocked but I can't sign any transactions:

    $ bitcoin-cli walletpassphrase "$x" 359711509437336257
    $ echo $?
    0
    $ bitcoin-cli signrawtransaction $tx | grep complete
    error code: -13
    error message:
    Error: Please enter the wallet passphrase with walletpassphrase first.

I don't know the significance of that number. It's nowhere near a power of 2.

I was trying to unlock the wallet effectively "forever", so put a big number. If I use too big a number (2^63 or more) I get an error message `JSON integer out of range` but for numbers between 359711509437336257 and 2^63-1 inclusive I get no error, but no actual unlocking.
+ HelpExampleRpc("listunspent", "6, 9999999 \"[\\\"1PGFqEzfmQch1gKD3ra4k18PNj3tTUUSqg\\\",\\\"1LtvqCaApEdUGFkpKMM4MstjcaL4dKg8SP\\\"]\"")
            + HelpExampleCli("listunspent", "6 9999999 '[]' true '{ \"minimumAmount\": 0.005 }'")
            + HelpExampleRpc("listunspent", "6, 9999999, [] , true, { \"minimumAmount\": 0.005 } ")
        );
    ObserveSafeMode();
    int nMinDepth = 1;
    if (!request.params[0].isNull()) {
        RPCTypeCheckArgument(request.params[0], UniValue::VNUM);
        nMinDepth = request.params[0].get_int();
    }
    int nMaxDepth = 9999999;
    if (!request.params[1].isNull()) {
        RPCTypeCheckArgument(request.params[1], UniValue::VNUM);
        nMaxDepth = request.params[1].get_int();
    }
    std::set<CTxDestination> destinations;
    if (!request.params[2].isNull()) {
        RPCTypeCheckArgument(request.params[2], UniValue::VARR);
        UniValue inputs = request.params[2].get_array();
        for (unsigned int idx = 0; idx < inputs.size(); idx++) {
            const UniValue& input = inputs[idx];
            CTxDestination dest = DecodeDestination(input.get_str());
            if (!IsValidDestination(dest)) {
                throw JSONRPCError(RPC_INVALID_ADDRESS_OR_KEY, std::string("Invalid Bitcoin address: ") + input.get_str());
            }
            if (!destinations.insert(dest).second) {
                throw JSONRPCError(RPC_INVALID_PARAMETER, std::string("Invalid parameter, duplicated address: ") + input.get_str());
            }
        }
    }